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?

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Answer 1 · 2018-05-28T14:55:09

After $13$ weeks

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

$J = 20+6w$

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

$A = 150 - 4w$

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

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

Add $4w$ to both sides:

$20+10w = 150$

Subtract $20$ from both sides:

$10w = 130$

Divide both sides by $10$ :

$w = 13$