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
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 = 180
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.
Answered On 06/27/2019 02:05
x= Christopher's money
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