Monica and Michael

Question

Monica and Michael both want to buy a scooter. Monica has already saved $25 and plans to save $5 per week until she can buy the scooter. Michael has $16 and plans to save $8 per week. In How many weeks will they have saved the same amount of money? How much money will they have saved? 

Answer 1

Hi Joanna!

We're first going to start by defining our terms. Monica has $25 and plans on saving $5 a week and Michael has $16 and plans on saving $8 a week. So we can set this equation up like:

Monica y = 5x + 25. (x represents the number of weeks and 25 is the amount of money she already has).

Michael z = 8x + 16 (x represents the number of weeks and 16 is the amount of money he already has.)

To combine those since the amounts should be equal, the new equation is 8x+16 = 5x + 25.

Solving steps:

8x-5x + 16 = 25

3x = 25-16

3x = 9

x = 3

So it will take Monica and Michael 3 weeks to save up the same amount of money. To calculate the amount that they will have, we'll plug the 3 into the spots where the x is in the initial two equations. So, 8(3) + 16 = 40 and 5(3) + 25 also equals 40.

3 weeks total to have the same amount of money, which is $40.

Hope this helps! If you need any clarification let me know!