# Question a0a33

Feb 25, 2018

$10$ weeks.

#### Explanation:

First, we want to turn the words into math equations. For equation $\left(1\right)$, let's set it equal to Roberto's piggy bank $\left(y\right)$

$y = 5 x + 30$

He starts off with $30 and adds $5$every week, or $5 x$where $x$is in weeks. The second equation for Jack this time, is he has $0$starting cash, and adds $8# every week or $8 x$, so his equation is

$y = 8 x + 0$

Next, set these two equations equal to each other to find out how many weeks $\left(x\right)$ the boys will have to wait to have the exact same amount of money.

$5 x + 30 = 8 x$

Subtract $5 x$ from both sides to keep it equal.

$30 = 3 x$

Divide by $3$ on both sides

$10 = x$

And you have your answer! After $10$ weeks, they will both have the same amount of money.