Christopher has six times as much money as Michael. If Michael earns $80 and Christopher earns $60, Christopher will then have three times as much money as Michael. How much money do Christopher and Michael have before and after earning $60 and $80, respectively?

Asked By Ana On 06/26/2019 19:19

Answers

Hello! Great question. I've always found it beneficial to use variables with these problems. For example, let's say: C = Christopher's initial money and M = Michael's initial money. Now let's convert the following sentences to algebra! "Christopher has six times as much money as Michael" can be represented as: C = 6M "If Michael earns $80 and Christopher earns $60, Christopher will then have three times as much money as Michael." can be represented as: C + 60 = (M + 80) x 3 Now, let's simplify this second equation and place it 'under' our first equation to create a system: C = 6M C = 3M + 180 (I skipped a few steps with simplifying the second equation) Now, we can use either substitution, elimination, or graphing to find our solutions for C and M. Since C is already isolated in both equations, let's use substitution, then solve! 6M = 3M + 180 -3M -3M 3M = 180 /3 /3 M = 60 Now that we know Michael's initial amount of money, we can substitute 60 in for M in either of the equations in our system. (Let's choose the easier one!) C = 6(60) C = 360 Therefore, Christopher had $360 initially, and Michael had $60 initially. Don't forget to check your answer by making sure these values work in the context of the problems first sentence, AND second problem. Thank you!
Answered On 06/27/2019 02:05


x= Christopher's money y=Michael's money x=6y x+60=3(y+80) 6y+60=3y+240 3y=180 y=60 Christopher has $360 and Michael has $60 After earning money, Christopher has $420 and Michael has $140. 420 = 3 x 140
Answered On 06/27/2019 15:43