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#