Percents

[maya2008]

I'm not so good at percents..it always confuses me
Here is a question from OG11TH Q115

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?

The answers are: A 124% B 120% C 96% D 80% E 64%

I was trying to substitute 100 as the whole. Anyone have an easier approach?

Thanks...

[fajoni]

Using 100 as your starting point was a good idea. It's important to realize that the question is essentially asking for Mary's income/Juan's income. Because this is a percent problem and Juan's income is the denominator, I made his income 100. Then I just worked backwards.

If J = $100, then T = $60 (forty percent less than 100 is 60 percent of 100.)

If T = $60, then M = 60 X 1.6 = $96.

Thus, $96/$100 shows you that M's income is 96% of J's income.

Hope this helps....good luck on the test!

[maya2008]

[II]

Using 100 as your starting point was a good idea. It's important to realize that the question is essentially asking for Mary's income/Juan's income. Because this is a percent problem and Juan's income is the denominator, I made his income 100. Then I just worked backwards.

If J = $100, then T = $60 (forty percent less than 100 is 60 percent of 100.)

If T = $60, then M = 60 X 1.6 = $96.

Thus, $96/$100 shows you that M's income is 96% of J's income.

Hope this helps....good luck on the test!

This is a good way of tackling this question. The key here is to understand what the question is asking.

Another approach is to solve this algebraically.

Assign variables:
m = mary income
t = tim income
j = juan income

"Mary's income is 60 percent more than Tim's income" can be written as:
m = 1.6t
"Tim's income is 40 percent less than Juan's income" can be written as:
t = 0.6j
"what percent of Juan's income is Mary's income?"
x/100 = m/j (where x is the percent we are looking for)

We can use "t = 0.6j" to find j ----> j = t/0.6.

plug-in the values for m and j ------> x/100 = 1.6t / (t/0.6)
cross multiply ------------------------> (x)(t/0.6) = (1.6t)(100)
simplify -------------------------------> xt/0.6 = 160t
multiply both sides by 0.6 (or 3/5)-> xt = 96t, so x = 96

This is just another approach ... but I would use Fajoni's approach for this. Much easier and quicker.