Walkabout wrote:
Mary's income is 60 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?
(A) 124%
(B) 120%
(C) 96%
(D) 80%
(E) 64%
To solve this problem we create variables for the income of Mary, Tim, and Juan, and then set up some equations.
T = Tim’s income
M = Mary’s income
J = Juan’s income
We are given that Mary’s income is 60% more than Tim’s. Thus, we can say:
M = 1.6T
We are also given that Tim’s income is 40% less than Juan’s income. So we can say:
T = 0.6J
We are asked to determine the percent of Juan’s income that Mary’s income is. For this we can set up the expression:
M/J x 100%
To complete this problem we must express Juan's income and Mary’s income in terms of a common variable. That common variable is T. Thus, we have:
M = 1.6T
J = T/0.6
So finally we can substitute T/0.6 for J and 1.6T for M
M/J x 100%
(1.6T)/(T/0.6) x 100%
(1.6T) x (0.6/T) x 100%
The T’s cancel and we have:
1.6 x 0.6 x 100%
0.96 x 100% = 96%
Answer C.
For some students, an easier way to solve this is to use convenient numbers. If we "pretend" that Juan's income is J = $100, and Tim's income is 40% less than Juan's, then Tim's income is: 100 – (100)(.40) = $60. We also are told that Mary's income is 60% more than Tim's: 60 + (60)(.60) = 60 + 36 = $96.
Now we can easily determine the percent of Juan's income that Mary's income represents: (96/100) x 100% = 96%.
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