Compare the two proportional relationships described below. Relation A is shown in the table: Relation B is represented by the equation $$y = 3x$$ . Which statement correctly compares the two relationships?

The relationships are the same because they both represent a ratio of $$3:1$$ .

The relationships are different because Relation B has a ratio of $$1:12$$ .

Two cleaning companies charge proportional rates for their services. Company A charges $$\$132$$ for $$6$$ hours of work. The rates for Company B are shown in the table below: Which company has a lower hourly rate and by how much?

Company A because it charges $$\$3.00$$ less per hour than Company B.

Company A because it charges $$\$2.00$$ less per hour than Company B.

Company B because it charges $$\$3.00$$ less per hour than Company A.

Company B because it charges $$\$2.00$$ less per hour than Company A.

Swift Shipping charges $$\$12.00$$ to ship an $$8$$ -pound package. The table below shows the costs for Quick Courier. Which shipping service is more expensive per pound, and by how much?

Swift Shipping is more expensive by $$\$0.25$$ per pound.

Quick Courier is more expensive by $$\$0.15$$ per pound.

Quick Courier is more expensive by $$\$0.25$$ per pound.

Swift Shipping is more expensive by $$\$0.15$$ per pound.

Leo and Mila are hiking on different trails. Leo hikes at a constant speed of $$4.5$$ miles every $$1$$ hour. The table below shows the distance Mila travels over time at a constant speed. Which statements correctly compare these two proportional relationships? Select all that apply.

Mila’s rate of speed is $$0.75$$ miles per hour faster than Leo’s rate of speed.

At their respective rates, Leo would travel $$13.5$$ miles in $$3$$ hours.

Leo’s rate of speed is $$2.25$$ miles per hour faster than Mila’s rate of speed.

At their respective rates, Mila would travel $$21.5$$ miles in $$4$$ hours.

The unit rate for Mila is $$4.25$$ miles per hour.

Two stores sell bulk flour by the pound. The tables below show the cost of flour at each store. Which statement correctly compares the unit rates of the two stores?

Store B has a higher unit rate of $$\\$0.85$$ per pound.

Store A has a higher unit rate of $$\\$0.80$$ per pound.

Both stores have an equivalent unit rate of $$\\$0.80$$ per pound.

Store B has a lower unit rate of $$\\$0.75$$ per pound.

A grocery store sells apples at a price described by the equation $$c = 1.50p$$ , where $$c$$ is the total cost and $$p$$ is the number of pounds. The store also sells pears for a total of $$\$5.80$$ for every $$4$$ pounds. Which statements comparing these two relationships are true? Select all that apply.

Buying $$5$$ pounds of apples costs $$\$0.25$$ more than buying $$5$$ pounds of pears.

The cost of $$10$$ pounds of apples is $$\$15.00$$ .

The price per pound of pears is greater than the price per pound of apples.

The unit rate for the pears is $$\$1.45$$ per pound.

The constant of proportionality for the apples is $$1.45$$ .

Two propane companies charge customers based on the number of gallons purchased. Company A uses the equation $$y = 1.35x$$ to determine the total cost, $$y$$ , for $$x$$ gallons of propane. The table below shows the costs for Company B. Which statement correctly compares the price per gallon between the two companies?

Company B charges $$\$0.15$$ more per gallon than Company A.

Company A charges $$\$1.10$$ more per gallon than Company B.

Company B charges $$\$1.35$$ more per gallon than Company A.

Company A and Company B charge the same amount per gallon.

Two companies charge for pressure washing services based on the number of hours worked. Company A charges a total of $$\\$56.00$$ for $$4$$ hours of work. The pricing for Company B is shown in the table below. Which company has the lower unit rate per hour, and what is that rate?

Company A because it charges $$\\$14.00$$ per hour.

Company A because it charges $$\\$12.50$$ per hour.

Company B because it charges $$\\$13.25$$ per hour.

Company B because it charges $$\\$15.00$$ per hour.

Two local moving companies charge a flat rate per mile for local deliveries. Company A charges a total of $$\$70.00$$ for a $$20$$ -mile delivery. The rates for Company B are shown in the table below. Which statement correctly compares the unit rates per mile of the two companies?

Company B charges $$\$1.50$$ more per mile than Company A.

Company A charges $$\$1.50$$ more per mile than Company B.

Company B charges $$\$0.50$$ more per mile than Company A.

Company A charges $$\$0.50$$ more per mile than Company B.

Company A pays employees a constant rate of $$\$33.00$$ for every $$2$$ hours of work. The earnings for Company B are shown in the graph below. Which company pays a higher hourly rate, and what is the difference between their hourly rates?

Company A, because its rate of $$\$16.50$$ per hour is greater than Company B's rate of $$\$12.50$$ per hour.

Company A, because its rate of $$\$16.50$$ per hour is greater than Company B's rate of $$\$15.00$$ per hour.

Company B, because its rate of $$\$20.00$$ per hour is greater than Company A's rate of $$\$16.50$$ per hour.

Company B, because its rate of $$\$15.00$$ per hour is greater than Company A's rate of $$\$12.50$$ per hour.

Two cleaning companies charge for their services based on the number of hours worked. Company A uses the rates shown in the table below. Company B charges a flat rate of $$\$27$$ per hour. Which company will charge more for a $$6$$ -hour job, and what is that cost?

Company B will charge $$\$162$$

Company A will charge $$\$135$$

Company A will charge $$\$162$$

Company B will charge $$\$150$$

Store A sells bulk flour as shown in the table below. Store B sells bulk flour at a rate of $$\$2.40$$ for every $$3$$ pounds. Using cross-multiplication or equivalent fractions to compare the unit rates, which statement correctly describes the relationship between the costs at the two stores?

The cost per pound at Store A is equal to the cost per pound at Store B because both ratios form a proportion.

The cost per pound at Store A is $$\$0.20$$ less than the cost per pound at Store B.

The cost per pound at Store A is $$\$0.40$$ more than the cost per pound at Store B.

The relationship at Store B is not proportional, so the costs per pound cannot be compared.

Company A charges a total of $$\$42.00$$ to deliver $$600$$ gallons of water. The table below shows the costs for water delivery from Company B. Which statements correctly compare the two water delivery companies? Select all that apply.

Company A charges $$\$0.02$$ more per gallon of water than Company B.

For both companies, the cost of $$1{}000$$ gallons of water is more than $$\$50.00$$ .

Company B charges less per gallon of water than Company A.

A delivery of $$500$$ gallons from Company A costs $$\$2.00$$ less than from Company B.

Company A charges exactly $$\$0.12$$ per gallon of water.

Two proportional relationships are represented by the equations below: Relationship A: $$y = 9x$$ Relationship B: $$y = 12x$$ Which statements correctly compare the rates of the two relationships? Select all that apply.

Relationship B has a greater unit rate than Relationship A because $$12 > 9$$ .

Relationship A has a smaller constant of proportionality than Relationship B.

Relationship A has a greater unit rate than Relationship B because $$9 > 0.75$$ .

The constant of proportionality for Relationship A is $$\frac{4}{3}$$ times the constant for Relationship B.

The constant of proportionality for Relationship B is $$3$$ units larger than the constant for Relationship A.

Two shipping companies calculate the cost of sending a package based on its weight in pounds. Company A uses the equation $$c = 3.35w$$ , where $$c$$ is the total cost in dollars and $$w$$ is the weight in pounds. The table below shows the costs for Company B: Which statement correctly compares the cost per pound between the two companies?

Company B is $$\$0.15$$ more expensive per pound than Company A.

Company A is $$\$0.15$$ more expensive per pound than Company B.

Company B is $$\$0.25$$ more expensive per pound than Company A.

Company A is $$\$0.25$$ more expensive per pound than Company B.

Two different companies offer hourly earnings for a project. The graph represents the relationship between the time worked and the total earnings for Company A. For Company B, the relationship is given by the equation $$y = 18x$$ , where $$y$$ is the total earnings in dollars and $$x$$ is the time in hours. Which company has the lesser unit rate, and what is that rate?

Company A, because its unit rate is $$\$15$$ per hour.

Company B, because its unit rate is $$\$18$$ per hour.

Company A, because its unit rate is $$\$30$$ per hour.

Company B, because its unit rate is $$\$9$$ per hour.

Tasty Treats sells frozen yogurt for $$\$0.45$$ per ounce. A second shop, Sweet Swirl, uses the pricing shown in the table below. Which statement correctly compares the unit rates of the two shops?

The price at Tasty Treats is $$\$0.05$$ more per ounce than the price at Sweet Swirl.

The price at Tasty Treats is $$\$0.10$$ less per ounce than the price at Sweet Swirl.

The price at Sweet Swirl is $$\$0.05$$ more per ounce than the price at Tasty Treats.

The price per ounce is the same at both shops.

Company A sells bulk coffee at a rate of $$\$40.50$$ for every $$6$$ pounds purchased. The pricing for Company B is shown in the table below. Which company offers the cheaper unit price, and by how much?

Company B is cheaper by $$\$0.15$$ per pound.

Company A is cheaper by $$\$0.15$$ per pound.

Company A is cheaper by $$\$0.50$$ per pound.

Company B is cheaper by $$\$0.50$$ per pound.

Two shops sell coffee beans by the pound. At Shop A, the cost of coffee beans is $$\$12.20$$ for every $$2$$ pounds. The costs at Shop B are shown in the table below. Which of the following statements comparing the two shops are true? Select all that apply.

The constant of proportionality for Shop B is $$0.2$$ greater than the constant of proportionality for Shop A.

Purchasing $$10$$ pounds of coffee at Shop B is $$\$2.00$$ more expensive than at Shop A.

The constant of proportionality for Shop A is $$0.5$$ greater than the constant of proportionality for Shop B.

Purchasing $$10$$ pounds of coffee at Shop A is $$\$2.00$$ cheaper than at Shop B.

The unit rate at Shop A is $$\$12.50$$ per pound.

Nadia's car travels $$464 \text{ miles}$$ on $$16 \text{ gallons}$$ of gas. The fuel efficiency of Aidan's car is represented by the equation $$d = 32g$$ , where $$d$$ is the distance in miles and $$g$$ is the number of gallons of gas. Which statement correctly compares the fuel efficiency, in miles per gallon, of the two cars?

Nadia's car is more fuel-efficient because $$29

Aidan's car is more fuel-efficient because $$32 > 29$$ .

Aidan's car is more fuel-efficient because $$32 > 2.9$$ .

Nadia's car is more fuel-efficient because $$3.2 > 2.9$$ .

Ship A travels at a constant speed described by the equation $$d = 20t$$ , where $$d$$ is the distance in miles and $$t$$ is the time in hours. Ship B travels at a constant speed of $$132$$ miles every $$6$$ hours. Which statements correctly compare the two proportional relationships?

Ship B is faster than Ship A because it travels $$2$$ more miles per hour.

Both ships will have traveled the same distance after $$0$$ hours.

Ship A is slower than Ship B because $$22 > 20$$ .

In $$5$$ hours, Ship A will travel $$10$$ more miles than Ship B.

Ship A travels at a unit rate of $$22$$ miles per hour.

A school is ordering customized t-shirts from two different companies. Company A charges based on the equation $$y = 12.5x$$ , where $$y$$ is the total cost and $$x$$ is the number of shirts. Company B uses the pricing shown in the table below. Which statement best justifies which company has a lower cost per shirt?

Company A is cheaper because $$12.5$$ is less than the $$13.5$$ unit rate of Company B.

Company A is cheaper because the equation has only one constant value.

Company B is cheaper because it charges $$\$27.00$$ for the first two shirts.

Company B is cheaper because the difference between the costs in the table is only $$\$40.50$$ .

A garden shop sells two types of soil. Soil A costs $$\$3.50$$ per bag. Soil B's cost is represented by a line on a graph that passes through the origin and the point $$(4, 12)$$ . Select the TWO statements that correctly compare these proportional relationships.

Soil A has a higher unit rate than Soil B.

The unit rate for Soil B is $$\$3.00$$ per bag.

Soil B has a higher unit rate than Soil A.

A 10-bag order of Soil A costs $5.00 more than a 10-bag order of Soil B.

A 10-bag order of Soil B costs $5.00 more than a 10-bag order of Soil A.

Jamie and Taylor are both saving money. Jamie's savings are represented by the equation $$s = 15w$$ , where $$s$$ is total savings and $$w$$ is weeks. Taylor's savings are shown in the table below. Taylor claims that he is saving more money per week than Jamie. Is Taylor's claim correct?

Yes, Taylor is correct because $$18 > 15$$ .

No, Taylor is incorrect because Jamie starts with $$\$15$$ and Taylor starts with $$\$0$$ .

Yes, Taylor is correct because $$\$54$$ is more than $$\$15$$ .

No, Taylor is incorrect because $$54 \div 3$$ is less than $$15$$ .

Two stores sell loose candy by the pound. Store A uses the table below to determine prices. Store B uses the equation $$c = 1.75p$$ , where $$c$$ is cost and $$p$$ is pounds. Select the THREE correct statements.

The unit rate for Store A is $1.50 per pound.

Store B is more expensive per pound than Store A.

At Store B, 10 pounds of candy costs $17.50.

Store A is more expensive per pound than Store B.

A 4-pound bag costs the same at both stores.

failed_NC.7.RP.2.a.iii - Question_bank

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Two different printers, Printer A and Printer B, print pages at constant rates. The tables below show the number of pages each printer can produce over different periods of time.
Which printer has the greater unit rate of pages per minute?

Tags

NC.7.RP.2.a.iii

DOK 2

Blooms Level: Apply

Compare two proportional relationships both rep...

MATH RESPONSE QUESTION

2 mins • 1 pt

Mathematical Equivalence

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NC.7.RP.2.a.iii

DOK 2

Blooms Level: Apply

Compare two proportional relationships both rep...

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Relation A has a higher unit rate than Relation B.

Relation B has a lower unit rate than Relation A.

Tags

NC.7.RP.2.a.iii

DOK 2

Blooms Level: Analyze

Identify a proportion as a statement of equalit...

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

NC.7.RP.2.a.iii

DOK 2

Compare two proportional relationships where on...

Blooms Level: Apply

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

NC.7.RP.2.a.iii

DOK 2

Compare two proportional relationships where on...

Blooms Level: Analyze

MATH RESPONSE QUESTION

2 mins • 1 pt

The table below shows the cost of bulk candy at Store A. The graph shows the cost of the same candy at Store B.
What is the positive difference between the unit rates, in dollars per pound, of the two stores?

Mathematical Equivalence

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NC.7.RP.2.a.iii

DOK 2

Compare two proportional relationships where on...

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45 sec • 1 pt

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NC.7.RP.2.a.iii

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failed_NC.7.RP.2.a.iii - Question_bank

Two different printers, Printer A and Printer B, print pages at constant rates. The tables below show the number of pages each printer can produce over different periods of time.Which printer has the greater unit rate of pages per minute?

The table below shows the cost of bulk candy at Store A. The graph shows the cost of the same candy at Store B.What is the positive difference between the unit rates, in dollars per pound, of the two stores?

Two stores sell bulk flour by the pound. The tables below show the cost of flour at each store.Which statement correctly compares the unit rates of the two stores?

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Popular Resources on Wayground

Discover more resources for Mathematics

Two different printers, Printer A and Printer B, print pages at constant rates. The tables below show the number of pages each printer can produce over different periods of time.
Which printer has the greater unit rate of pages per minute?

The table below shows the cost of bulk candy at Store A. The graph shows the cost of the same candy at Store B.
What is the positive difference between the unit rates, in dollars per pound, of the two stores?

Two stores sell bulk flour by the pound. The tables below show the cost of flour at each store.
Which statement correctly compares the unit rates of the two stores?