Question

1. the number of tiles needed for a bathroom floor is proportional to the area of the bathroom floor. five tiles cover an area of 90 square inches. the bathroom floor has a total area of 3,024 square inches. let n be equal to the total number of tiles needed for the floor. set up and solve a proportion to find the value of n.

1. colton is taking a long bike ride where he rides at a constant speed. the distance he bikes is proportional to the amount of time he has been biking. after 3.5 hours, he has traveled a distance of 49 miles.

(a) find the ratio of the distance colton has traveled to the amount of time he has been traveling. express this as a unit rate and use appropriate units. what does this rate represent?

(b) colton travels at the same rate as in (a) for 6 hours. let d be the distance he biked. set up and solve a proportion for d.
(c) colton would like to bike 200 miles. let h be the number of hours it will take colton to bike this distance. solve a proportion for h. round to the nearest tenth of an hour.

n-gen math® 7, unit 3 - proportional relationships - lesson 6
emathinstruction, red hook, ny 12571, © 2020

Explanation:

Problem 4

Step1: Set up proportional ratio

$\frac{\text{Number of tiles}}{\text{Area}} = \frac{5}{90} = \frac{n}{3024}$

Step2: Simplify the ratio

$\frac{1}{18} = \frac{n}{3024}$

Step3: Solve for $n$

$n = \frac{3024}{18}$

Step1: Calculate distance-time ratio

$\frac{49 \text{ miles}}{3.5 \text{ hours}}$

Step2: Simplify to unit rate

$\frac{49}{3.5} = 14$

Step1: Set up speed proportion

$\frac{49}{3.5} = \frac{d}{6}$

Step2: Substitute unit rate

$14 = \frac{d}{6}$

Step3: Solve for $d$

$d = 14 \times 6$

Answer:

$n = 168$

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Problem 5

Part (a)