Solving Problems Involving Proportions

Solving Problems Involving Proportions

Cost of a Pizza

Opening

Cost of a Pizza

Let p equal the price in dollars of one Super Combo pizza.

  • Write an equation that you could use to find that price.
  • How much does each pizza cost?

Math Mission

Opening

Write and solve equations in order to solve real-world mathematical problems.

The Track Team

Work Time

The Track Team

There are 78 girls on the track team. This is 5 more than the number of boys on the team. How many boys are on the track team?

  • Choose a variable to represent what you want to find out.
  • Write an equation that you can use to solve the problem.
  • Solve the equation.
  • Think about your answer. Does it make sense? Explain.

Hint:

Let b = the number of boys on the team. What expression has the same value as 78?

Write and Solve Equations

Work Time

Write and Solve Equations

The product of 23 and a number is 14.

  • Choose a variable to represent what you want to find out.
  • Write an equation that you can use to solve the problem.
  • Solve the equation.
  • Think about your answer. Does it make sense? Explain.

Hint:

  • Choose a variable such as n to represent the number.
  • What equation can you write?
  • Think about whether your answer should be greater than or less than 14.

Mixing Paint

Work Time

Mixing Paint

Carlos mixed some green paint by using 4 cups of blue paint and 3 cups of yellow paint. He used all of the green paint and wants to make some more. How many cups of blue paint should he mix with 5 cups of yellow paint to get the same color green?

  • Choose a variable to represent what you want to find out.
  • Write an equation that you can use to solve the problem.
  • Solve the equation.
  • Think about your answer. Does it make sense? Explain.

Hint:

  • What proportion represents the problem?
  • Where will you put the 5 in the proportion?
  • What will you multiply or divide by to make the equation easier to work with?

Cost of Cheese

Work Time

Cost of Cheese

If 3 lb of cheese cost $7, how many pounds of the same cheese can you buy for $25?

  • Choose a variable to represent what you want to find out.
  • Write an equation that you can use to solve the problem.
  • Solve the equation.
  • Think about your answer. Does it make sense? Explain.

Hint:

  • What proportion represents the problem?
  • Where will you put the 25 in the proportion?

Prepare a Presentation

Work Time

Prepare a Presentation

Choose one of the word problems from this lesson to present.

  • Explain how you came up with your equation or inequality.
  • Explain the steps you took to solve it.

Challenge Problem

Several friends share a pizza. The price of a plain cheese pizza is $13.00. Each additional topping costs $2.25. The friends pay $24.25 for their pizza.

  • Write an equation to represent this situation and then solve it to find out how many additional toppings are on the pizza.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about the approaches your classmates used to write equations to solve the problems.

Hint:

As your classmates present, ask questions such as:

  • Describe the process that you used to write the equation and solve it.
  • How did you decide where to put the 25 in the proportion?
  • Is that the only correct way to write the proportion?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

When I write an equation for a problem, I …