Proportions: word problems

Proportions: word problems

How to use proportion to solve everyday problems.

Review: Cross Multiplication

• The butterfly or cross multiplication method can be used to find the missing value of proportion.

• Multiply diagonally; setting each cross equal to each other.

• Divide both sides by the value with the variable.

• This will give the answer to a true proportion.

Proportions: How to set up to show equivalence

• When there are units of measurement involved, the same units should be across from each other in the proportion.

• Example:

   $\frac{50\ miles}{2\ hours}\ =\ \frac{100\ miles}{4\ hours}$  

• Notice the units of measurement are alike directly across from the other value.

•  $\frac{miles}{hours}\ =\ \frac{miles}{hours}$  

Example: set the proportion from the given ratios.

• 34 buttons to 3 shirts is equal to 11.5 buttons to 1 shirt

• Putting these into fraction form will set them up as equivalent proportions.

•  $\frac{34\ buttons}{3\ shirts}\ =\ \frac{11.5\ buttons}{1\ shirt}$  

• What do you notice about the units of measurement?

Word problems using proportion

• Understanding the correct set up of the rates or ratios in proportion form will help when you need to solve proportion problems.

• Example: If 6 melons cost $9, what is the cost of 10 melons?

• The rates are 6 melons to $9 is equal to 10 melons to x dollars.

• Set the proportion up; solve to find the cost of 10 melons.

Answer to the melon problem:

 $\frac{6\ melons}{\text{}9\ dollars}\ =\ \frac{10\ melons}{x\ dollars}$  
Cross multiply: 6(x) = 9(10)
         6x = 90
Divide by 6:  x = 15
It will cost $15 for 10 melons

You try: A person weighs 150 lbs on earth weighs about 25 lbs on the moon. How much would a person weigh on earth if their weight on the moon is 32 lbs?

•  $\frac{150\ lbs}{25\ lbs}\ \ \ =\ \ \frac{m\ lbs}{32\ lbs}$  

• 150 x 32= 25 x m

• 4800 = 25m

• 192 = m

• A person would weigh 192 lbs on earth if they weighed 32 lbs on the moon.

Multiple Choice

The pair of figures is similar. Find the missing side.

• x = 9
• x = 4
• x = 13
• x = 36

Multiple Choice

The pair of figures is similar. Find the missing side.

• x = 20
• x = 12
• x = 5
• x = 4

Multiple Choice

A cake recipe calls for 1.5 cups of milk and 3 cups of flour. Seth made a mistake and used 5 cups of flour. How many cups of milk should he use to keep the proportions correct?

• 2.5 cups milk
• 1.75 cups milk
• 2 cups flour
• 2.25 cups milk

Multiple Choice

A scale model of a whale is being built. The actual length of the whale is 65 feet. The scale of the model is 2 in : 3 ft. What will be the length of the model?

• 97.5 inches
• 30.6 inches
• 41.56 inches
• 43.33 inches

Multiple Choice

A rectangular garden is 45 ft wide and 70 ft long. In a drawing, the width is 9 in. Identify the length on the drawing. 

• 7 in
• 9 in
• 12 in
• 14 in

Multiple Choice

About 13 out of 20 homes have a personal computer. On a street with 60 homes, how many computers would you expect to have?

• 39 Computers
• 4.3 Homes
• 39 Homes
• 4.3 Computers

Multiple Choice

Hamburger meat sells for $6 for every 3 pounds. If Alicia buys 10 pounds of hamburger meat, how much will she pay?

• $30
• $20
• $60
• $10

Multiple Choice

12 ounce shampoo bottle lasts Mike 16 weeks.  How long would you expect an 18-ounce bottle of the same brand to last him?

• 24 weeks
• 6 weeks
• 30 weeks
• 20 weeks

Multiple Choice

Solve for x 

• x = 1/10
• x = 10
• x = 4
• x = 5

Multiple Choice

Pat needs 14 sticks of pepperoni to make 28 pizzas.  How many sticks of pepperoni are needed to make 36 pizzas?  

• 15 pizzas
• 252 sticks
• 18 sticks
• 18 pizzas

Multiple Choice

If four ice creams cost $3.20, what would 8 ice cream cost?

• $7.20

• $6.40

• $10.00

• $9.60

Multiple Choice

6 pencils costs 36 cents. How much do 2 pencils cost?

• 6

• 12

• 3

• 8

Multiple Choice

Four pounds of apples cost $5.00. How much would 10 pounds of apples cost?

• I'm hungry
• $15.75
• $10
• $12.50

Multiple Choice

I have read 146 pages in 3 hours. How long would it take to read an entire 390 page book?

Choose the correct proportion.

•  $\frac{146\ pages}{3\ hours\ }=\frac{390\ pages}{x\ hours}$ 

•  $\frac{146\ pages}{390\ pages\ }=\frac{x\ hours}{3\ hours}$ 

•  $\frac{146\ pages}{x\ hours\ }=\frac{390\ pages}{3\ hours}$ 

•  $\frac{3\ hours}{x\ hours\ }=\frac{390\ pages}{146\ pages}$ 

Multiple Choice

Emily's original painting has a width of 3 inches and a height of 4 inches. She enlarged the size of the painting so that it has a width of 15 inches. What is the new height?

Which of these proportions correctly represents the situation?

• $\frac{3\ in\ width}{4\ in\ height}=\frac{15\ in\ width}{x\ in\ height}$

• $\frac{3\ in\ width}{15\ in\ height}=\frac{4\ in\ width}{x\ in\ height}$

• $\frac{3\ in\ width}{5\ in\ height}=\frac{4\ in\ width}{15\ in\ height}$

• $\frac{3\ in\ width}{4\ in\ height}=\frac{x\ in\ height}{15\ in\ width}$

Multiple Choice

Ms. Hensley's family owns a green bean farm. If Ms. Hensley can grow 225 bushels in 3 acres, how many bushels can she grow in 9.6 acres?

• 720 bushels

• 675 bushels

• 75 bushels