Question

A college student realized that he was spending too much money on music. For the remaining 5 months of the year his goal is to spend a mean of $50 a month towardsmusic. How much can he spend in December, taking into consideration that in the other 4 months he spent $20, $70, S30, and $85, respectively? Round your answerto two decimal places. If necessary

Answer 1

The mean is given by the sum of all the months divided by the number of months.

Then:

Let's set x for the spending money for December.

There are 5 months.

Hence:

$\operatorname{mean}=\frac{20+70+30+85+x}{5}$

We need to have a mean equal to $50. Set mean = 50.

$50=\frac{20+70+30+85+x}{5}$

Solve for x:

$\begin{gathered} 50=\frac{20+70+30+85+x}{5} \\ 50=\frac{205+x}{5} \\ 5\cdot50=205+x \\ 250=205+x \\ \text{Therefore:} \\ x=250-205 \\ x=45 \end{gathered}$

Hence, If the student wants to complete his goal, he will need to spend $45 in December.