Lesson 3

Revisiting Proportional Relationships

Let’s use constants of proportionality to solve more problems.

Problem 1

It takes an ant farm 3 days to consume \(\frac12\) of an apple. At that rate, in how many days will the ant farm consume 3 apples?

Problem 2

To make a shade of paint called jasper green, mix 4 quarts of green paint with \(\frac23\) cups of black paint. How much green paint should be mixed with 4 cups of black paint to make jasper green?

Problem 3

An airplane is flying from New York City to Los Angeles. The distance it travels in miles, \(d\), is related to the time in seconds, \(t\), by the equation \(d=0.15t\). 

  1. How fast is it flying? Be sure to include the units.
  2. How far will it travel in 30 seconds?
  3. How long will it take to go 12.75 miles?

Problem 4

A grocer can buy strawberries for $1.38 per pound.

  1. Write an equation relating \(c\), the cost, and \(p\), the pounds of strawberries.
  2. A strawberry order cost $241.50. How many pounds did the grocer order?

Problem 5

Crater Lake in Oregon is shaped like a circle with a diameter of about 5.5 miles.

  1. How far is it around the perimeter of Crater Lake?

  2. What is the area of the surface of Crater Lake?

(From Unit 3, Lesson 10.)

Problem 6

A 50-centimeter piece of wire is bent into a circle. What is the area of this circle?

(From Unit 3, Lesson 8.)

Problem 7

Suppose Quadrilaterals A and B are both squares. Are A and B necessarily scaled copies of one another? Explain.

(From Unit 1, Lesson 2.)