# Janelle has $20 and is saving$6 per week. April has $150 and is spending$4 per week. When will they both have the same amount of money?

May 28, 2018

After $13$ weeks

#### Explanation:

Janelle starts with $20$, and gains $6$ per week. So, after $w$ weeks, she will have gained $6 w$, for a total amount of

$J = 20 + 6 w$

Similarly, April starts with $150$, and loses $4$ per week. So, after $w$ weeks, she will have lost $4 w$, for a total amount of

$A = 150 - 4 w$

We wonder when they will have the same amount of money, so:

$J = A \setminus \iff 20 + 6 w = 150 - 4 w$

Add $4 w$ to both sides:

$20 + 10 w = 150$

Subtract $20$ from both sides:

$10 w = 130$

Divide both sides by $10$:

$w = 13$