Computer Project

Suppose Jenny and Rachel are going to go to the mall when they have the same amount of money. Right now, Jenny has $60 but spends $8 every week. At the same time, Rachel has $15 but makes $7 every week. How many weeks will it take them to get the same amount of money and how much money will they have?

Let y=amount of money

Let x=# of weeks

y=60-8x

y=15+7x

60-8x=15+7x

-15 +8x= -15 +8x

45=15x

15=15

3=x

y=60-8(3)

y=60-24

y=36

y=15+7(3)

y=15+21

y=36

Answer: It will take 3 weeks and they will have $36.

When you first attempt a problem make sure you have a full understanding of it. Then you want to make an equation but first make sure to define your variables. In my equations I let y=amount of money and let x=number of weeks. I then created two equations, one for Jenny and one for Rachel. My equation for Jenny was y=60-8x because she has $60, and is losing $8 per week. The equation I came up with for Rachel was y=15+7x because she has $15 and is earning $7 per week. Since they are going to both equal the same amount of money, I used substitution and did 60-8x=15+7x. I then subtracted 15 from each side and added 8x to each side to get variables on one side and numbers on the other. I then got 45=15x. Because I wanted to get x alone, I divided each side by 15 and got x=3. Now I figured out that it would take 3 weeks for them to get the same amount of money. To check my answer I plugged 3 into the x position. In both equations y=36 so I knew my answer was correct. My final answer was that it would take Jenny and Rachel 3 weeks, and they would have $36.