Question

1. in a week, tracy earns $12.45 less than twice the amount kayla earns. tracy earns $102.45. how much does kayla earn? 17. solve the equation $2x + 4\frac{1}{5} = 9$. explain the ste and properties you used.

Explanation:

Question 16

Step1: Define variable for Kayla's earnings

Let \( x \) be the amount Kayla earns.

Step2: Write the equation based on the problem

Tracy earns \( \$12.45 \) less than twice Kayla's earnings, and Tracy earns \( \$102.45 \). So the equation is \( 2x - 12.45 = 102.45 \).

Step3: Solve for \( x \)

Add \( 12.45 \) to both sides: \( 2x = 102.45 + 12.45 = 114.9 \).
Divide both sides by 2: \( x = \frac{114.9}{2} = 57.45 \).

Step1: Subtract \( 4\frac{1}{5} \) from both sides

The equation is \( 2x + 4\frac{1}{5} = 9 \). First, convert \( 4\frac{1}{5} \) to decimal, which is \( 4.2 \). Subtract \( 4.2 \) from both sides: \( 2x = 9 - 4.2 = 4.8 \). (We use the Subtraction Property of Equality: if \( a = b \), then \( a - c = b - c \).)

Step2: Divide both sides by 2

Divide both sides of \( 2x = 4.8 \) by 2: \( x = \frac{4.8}{2} = 2.4 \). (We use the Division Property of Equality: if \( a = b \), then \( \frac{a}{c} = \frac{b}{c} \) for \( c
eq 0 \).)

Answer:

Kayla earns \(\$57.45\).

Question 17