Question

Grace earns $7 for each car she washes. She always saves $25 of her weekly earnings. This week, she wants to have at least $65 in spending money. How many cars must she wash? Enter and solve an inequality to represent this situation. Enter your value as a simplified mixed number, if necessary.

Answer 1

She must wash at least 13 cars

Explanation:

let:

`T_m=Money\hspace{3}earned\hspace{3}per\hspace{3}car\hspace{3}washed\\S=Money\hspace{3}for\hspace{3}savings\\S_m=Spending\hspace{3}money`

Now, mathematically we can define:

`T_m=7n\\S=constant=25\\S_m=T_m-S=7n-25`

Where:

`n=Number\hspace{3}of\hspace{3}cars\hspace{3}washed`

Now, we need to express the situation as a inequality. In this case, she wants to have at least $65 in spending money, so the inequality can be written as:

`T_m-S\geqslant S_m\\7n-25\geqslant65`

Solving for n:

add 25 to both sides:

`7n-25+25\geqslant65+25\\7n\geqslant90`

divide both sides by 7:

`(7)/(7) n \geqslant(90)/(7) \\n\geqslant 12.85714286`

`12.85714286\approx 13`

Therefore, Grace must wash at least 13 cars in order to have $65 in spending money