8.4 Proportion Word Problems

Ratio Reminders

• Don't forget to reduce your fractions!

• We will typically use fractions when discussing ratios and proportions.

• Double check to make sure you're in the same unit measure!!!

Proportions

• When two or more ratios are equivalent

• "Proportional" means that both ratios should reduce to the same fraction

Solving Proportions

• Notice that once you are done, the ratios reduce to the same fraction and the cross-products are equal (18=18)

Multiple Choice

What is a proportion?

• When two ratios can be simplified

• When two ratios are equivalent and show the same value

• When two ratios have the exact same numbers

• When two ratios can be multiplied by 2

Multiple Choice

Solve the proportion then check your answer by looking at their cross-products

• c = 4

• c = 8

• c = 14

• c = 10

Multiple Choice

Try another: Solve for x

• x = 16

• x = 28

• x = 135

• x = 26

Proportions

Other problems can be a bit more difficult to think about so we can use proportions to solve them. Review the picture before moving onto the next slide

Multiple Choice

What are the three steps to follow when setting up proportions?

• WKU

• WCU

• WUK

Multiple Select

What does WKU stand for?

choose all that apply

• Words

• Known

• Unnoticed

• Unknown

Multiple Choice

Ngozi can read 146 pages in 3 hours. How long would it take her 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

Baylee'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

A 6-ounce package of fruit snacks contains 45 pieces. How many pieces would you expect in a 10-ounce package? What is a correct way to setup the proportion?

• $$\frac{6}{45}=\frac{10}{x}$$

• $$\frac{10}{45}=\frac{6}{x}$$

Multiple Choice

A shop produces 39 wetsuits every 2 weeks. How long will it take the shop to produce 429 wetsuits? Setup then solve a proportion.

• 18 wk

• 20 wk

• 22 wk

• 24 wk

Multiple Choice

Jordyn bought 50 apples that cost $25. How much would 75 apples cost?

• $36.50

• $37.50

Multiple Choice

It takes Daniel 18 minutes to finish reading 4 pages of a book.

How long does it take for him to finish reading 30 pages?

• 135 minutes

• 120 minutes

Multiple Choice

Aliyah packs 25 boxes in 2 hours.

How many boxes can she pack in her 8-hour shift?

• 100 boxes

• 200 boxes

Multiple Choice

Brooks has a rectangular garden that is 45 ft wide and 70 ft long. In a drawing, the width is 9 in. What is the length on the drawing?

• 7 in

• 9 in

• 12 in

• 14 in

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 Makenzie 16 weeks.  How long would you expect an 18-ounce bottle of the same brand to last her?

• 24 weeks

• 6 weeks

• 30 weeks

• 20 weeks

Multiple Choice

Jesse 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

Taylor bought 6 pencils for 36 cents. How much do 2 pencils cost?

• 6

• 12

• 3

• 8

Multiple Choice

Sultan bought four pounds of apples that cost $5.00. How much would 10 pounds of apples cost?

• I'm hungry

• $15.75

• $10

• $12.50

Multiple Choice

Derrwin's car can go 210 miles on 4 gallons of gas, how far can it go on 12 gallons of gas?

• 630 miles

• 2,520 miles

• 70 miles

Multiple Choice

If 3 oranges cost $1.75, how much would 20 oranges cost?

• $35.00 for 20 oranges

• $11.66 for 20 oranges

• $20.00 for 20 oranges

Multiple Choice

Josiah burned 120 calories on a 1.6 km run. How many calories would they burn on a 5 km run?

• 490 calories

• 600 calories

• 375 calories

Multiple Choice

Levent and Landon need 8 oz of chocolate chips to make 1.6 lbs of cookie dough, how many ounces of chocolate chips will they need to make 7 pounds of cookie dough?

• 35 oz

• 56 oz

• 43 oz