Question

1. karen used one - third of her total stamps on a campaign for charity. karen used 60 stamps on the charity campaign.

a. write an equation you could use to find how many stamps she had at the start. choose any letter for the variable and explain what it represents.

b. solve the equation. how many stamps did karen start with?

1. denise used 22.5 gallons of water in the shower. this amount is 7.5 gallons less than the amount she used for washing clothes. write and solve an equation to find the amount of water x denise used to wash clothes.

1. in a visit to glacier national park in montana, vera hiked a total of 138 miles in 12 days. she hiked the same distance each day. write and solve an equation to find the number of miles m she hiked each day.

1. the temperature dropped 20 degrees from noon to midnight. the temperature at midnight was 24 °f. write and solve an equation to find the temperature at noon.

Explanation:

Question 7

Part A

Step1: Define variable

Let \( s \) represent the total number of stamps Karen had at the start.

Step2: Form equation

One - third of her total stamps is equal to the number of stamps used (60). So the equation is \(\frac{1}{3}s = 60\). The variable \( s \) represents the total number of stamps Karen had initially.

Step1: Solve for \( s \)

To solve \(\frac{1}{3}s=60\), we multiply both sides of the equation by 3.
\( 3\times\frac{1}{3}s=60\times3 \)

Step2: Simplify

Simplifying the left - hand side, \( 3\times\frac{1}{3}s = s \), and the right - hand side, \( 60\times3=180 \). So \( s = 180 \).

Step1: Define variable and form equation

Let \( x \) be the amount of water (in gallons) Denise used to wash clothes. The amount of water she used in the shower (22.5 gallons) is 7.5 gallons less than the amount she used for washing clothes. So the equation is \( x-7.5 = 22.5 \).

Step2: Solve for \( x \)

Add 7.5 to both sides of the equation: \( x-7.5 + 7.5=22.5 + 7.5 \)
Simplifying both sides, we get \( x=30 \).

Answer:

Equation: \(\boldsymbol{\frac{1}{3}s = 60}\), where \( s \) is the total number of stamps Karen had at the start.

Part B