Question

Erica earns $\$72$ for every $8$ hours she spends at the magic show. She earns $\$60$ for every 5 hours she spends at school. For every $3$ hours she spends at school, she spends $2$ hours at the magic show. Erica spends $15$ hours at school. How much money does she earn in January?

• A. $\$270$
• B. $\$90$
• C. $\$72$
• D. $\$180$

Answer 1

The correct option is A $\$270$

Given the ratio of time spent at school to the time spent at magic show is $3:2$.
Let us suppose Erica spends $x$ hours at the magic show, if she spends $15$ hours at school in January.

So, $\frac{3}{2}=\frac{15}{x}$

$x=\frac{(15\times 2)}{3}=10$

So, Erica spends 10 hours at the magic show, if she spends $15$ hours at school in January.

Earning from school in $5$ hours $=\$60$
Earning from school in $1$ hour $=\$\frac{60}{5}$
Earning from school in $15$ hours $=\frac{(15\times 60)}{5}=\$180$

Earning from magic show in $8$ hours $=\$72$
Earning from magic show in $1$ hour $=\$\frac{72}{8}$
Earning from magic show in $10$ hours $=\frac{(72\times 10)}{8}=\$90$

So, the total amount earned by Erica in January is $180+90=\$270$.
Hence, option B is correct.