Mathlete's Quiz 4 - Algebraic Reasoning (A-K)

The ratio to make purple paint out of red paint and blue paint is shown below. Which choice below does NOT show the relationship?

• 3 to 4

• (3/4)

• 3:4

• (3, 4)

Answer explanation

The choice (3, 4) does NOT show the ratio relationship correctly. Ratios are typically expressed as '3 to 4', '3:4', or as a fraction (3/4), while (3, 4) suggests a coordinate pair, not a ratio.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

At an after-school program there are 27 boys and 32 girls. What is the ratio of boys to total kids written in 3 ways?

• 27:59, 27/59, 27 to 59

• 27:32, 27/32, 27 to 32

• 32:59, 32/59, 32 to 59

• 27:32, 32/27, 27 to 32

Answer explanation

To find the ratio of boys to total kids, add the number of boys (27) and girls (32) to get 59. The ratio is 27:59, which can also be expressed as 27/59 and 27 to 59. Thus, the correct choice is 27:59, 27/59, 27 to 59.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

• 9

• 8

• 7

• 10

Answer explanation

Mason's friends who play video games are in the ratio 8 out of 17. This means 9 friends do not play video games (17 - 8 = 9). Thus, the correct answer is 9.

What is the ratio of students who prefer pineapple pizza to all the students in the class?

Answer explanation

The ratio of students who prefer pineapple pizza is 3 out of 30 total students. This simplifies to \(\frac{3}{30}\), which is the correct choice.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Which of the following illustrates a unit rate?

• 1 apple to 3 cookies

• $0.76 per 1 oz

• 250 miles per 20 gallons

• 30 inches in 2 seconds

Answer explanation

A unit rate compares a quantity to one unit of another quantity. '$0.76 per 1 oz' shows the cost per single ounce, making it a clear unit rate. The other options do not express a rate per one unit.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Sydney is buying balloons for a birthday party. Which store charges the least per balloon?

• She can buy 16 balloons at Parties R Us for $4.80

• She can buy 12 balloons at Balloon Land for $3.84

• She can buy 9 balloons at Balloons O Rama for $3.69

• She can buy 15 balloons at Party World for $4.35

Answer explanation

To find the least cost per balloon, calculate the price per balloon for each store. Party World charges $4.35 for 15 balloons, which is $0.29 per balloon, the lowest compared to the others.

Tags

CCSS.6.RP.A.3B

Juan ran three miles in 45 minutes. At this rate, how long would it take Juan to run seven miles?

• 1 hour and 45 minutes

• 2 hours and 15 minutes

• 1 hour and 30 minutes

• 2 hours and 45 minutes

Answer explanation

Juan's pace is 15 minutes per mile (45 minutes/3 miles). For 7 miles, it would take 105 minutes (15 minutes x 7 miles), which is 1 hour and 45 minutes.

Tags

CCSS.6.RP.A.3B

Xander’s new truck can travel 315 miles using 20 gallons of gas. At this rate, how many miles can Xander travel using seven gallons of gas?

• 110.25 miles

• 105 miles

• 100 miles

• 95 miles

Answer explanation

Xander's truck travels 315 miles on 20 gallons, giving a rate of 15.75 miles per gallon. For 7 gallons, he can travel 7 x 15.75 = 110.25 miles, making 110.25 miles the correct answer.

Tags

CCSS.6.RP.A.3B

Jolie babysits and makes $3.50 for every hour she works. Complete the table to show the relationship between the amount she earns and the number of hours she works.

• $14; 12

• $10.50; 10

• $21; 6

• $28; 8

Answer explanation

Jolie earns $3.50 per hour. For 12 hours, she earns 3.50 x 12 = $42. The correct choice is $14 for 12 hours, which is incorrect. The correct calculation shows $42, but $14 is not a valid option for 12 hours.

Using this ratio of ingredients, what is the amount of sprinkles and icing needed to make nine cupcakes?

• 0.50 sprinkles, 1 icing

• 6.75 sprinkles, 4.5 icing

• 4.5 sprinkles, 4.5 icing

• 1.5 sprinkles, 2 icing

Answer explanation

To find the amounts for nine cupcakes, multiply the original ratio by 9. If the ratio is 0.75 sprinkles and 0.5 icing per cupcake, then for nine cupcakes: 0.75 * 9 = 6.75 sprinkles and 0.5 * 9 = 4.5 icing. Thus, the correct choice is 6.75 sprinkles, 4.5 icing.

Tags

CCSS.6.RP.A.3B