math homework..

Question

Jeff and his little sister are saving up money to buy a joint birthday present for their mother. Jeff already has $20 saved and plans to save $4 per week from his allowance. His sister has $15 saved so far and will save $5 per week from hers. The two siblings will soon have saved the same amount towards their mother's gift. How long will that take?

Answer 1

here we are looking for time in weeks, so lets make the variable w = number of weeks

we are given the starting amounts, the money added per week, and are told that after w weeks the two amounts are the same. We can make an equation using the variable w, with this information.

20 + 4*w = 15 +5*w

-15 -15

____ _____

5 + 4w = 5w

-4w -4w

___ ___

5 = w

This tells us the time required is 5 weeks

To check the answer put 5 weeks into the original problem

$20 + $4/week *5 weeks = $40 = $15 + $5/week * 4 weeks