Question

Lydia received her salary on Friday. She spent one-half of her salary on rent and then spent $168 on her electric and water bill. Next she spent one-half of what was left on her phone bill. After spending $57.00 on gas for her car, Lydia had $92.00 left. How much did Lydia spend on rent?

A. $298
B. $466
C. $764
D. $932

Answer 1

B. $466

Explanation:

`\textsf{let}\: x= \textsf{Lydia's salary}`

`\implies \textsf{rent}=(1)/(2)x`

Modelling the given information to find the total salary:

`\implies \left(x-(1)/(2)x-168\right)-(x-(1)/(2)x-168)/(2)-57=92`

`\implies (1)/(2)x-168-((1)/(2)x-168)/(2)-57=92`

`\implies (1)/(2)x-((1)/(2)x-168)/(2)=317`

`\implies x-((1)/(2)x-168)=634`

`\implies x-(1)/(2)x+168=634`

`\implies (1)/(2)x=466`

`\implies x=932`

Therefore, Lydia's total salary was $932

`\implies \textsf{rent}=(1)/(2)(932)=\$466`

Answer 2

• B) $466

Explanation:

Let the amount of rent is R

Calculate the value of R in reverse order of spending

• R = (92 + 57)*2 + 168 = 466

Correct choice is B