Chris saved [tex] x [/tex] dollars and spent half of his savings buying video games. After earning an additional [tex] \$20 [/tex] cutting grass, he had [tex] \$60 [/tex]. If the equation [tex] \frac{1}{2} x + 20 = 60 [/tex] represents the scenario, how much did he start with in his savings?

A. [tex] \$20 [/tex]
B. [tex] \$40 [/tex]
C. [tex] \[tex]$80 [/tex]
D. [tex] \$[/tex]160 [/tex]



Answer :

To find how much Chris originally saved, we need to solve the equation:

[tex]\[ \frac{1}{2} x + 20 = 60 \][/tex]

Here’s the step-by-step solution:

1. Isolate the term involving [tex]\(x\)[/tex]:
- Subtract 20 from both sides of the equation.

[tex]\[ \frac{1}{2} x + 20 - 20 = 60 - 20 \][/tex]

Simplify both sides:

[tex]\[ \frac{1}{2} x = 40 \][/tex]

2. Solve for [tex]\(x\)[/tex]:
- To eliminate the fraction, multiply both sides of the equation by 2.

[tex]\[ 2 \cdot \frac{1}{2} x = 2 \cdot 40 \][/tex]

Simplify both sides:

[tex]\[ x = 80 \][/tex]

So, Chris originally saved [tex]\(\$ 80\)[/tex]. Therefore, the correct answer is:

[tex]\[ \boxed{80} \][/tex]