Marys income is 60% more than Tims income, and Tims income is 40 less than Juans income. What percent of Juans income is Mary's income?
a) 124
b)120
c)96
d)80
e)64
OG 115
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What if instead you assumed Tim's income is 100...aatech wrote:Assuming Tim's income is 40 PERCENT less than Juan's
Suppose Juan income is 100
Tim's income = 60
Mary's income = 60 + (60*60/100) = 96
Mary's income is 96% of Juan's
Do confirm if my assumption is right
Tim's income = 100
Mary's income = 160
Juan = 140
Juan is then 12.5% less then Mary's income.
I know this approach is wrong because it does not lead to the OA but can you please explain where I made my mistake?
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Where you made your mistake is with Juan = 140. When Tim is 40% less than Juan, that does not mean that Juan = 140% of Tim.What if instead you assumed Tim's income is 100...
Tim's income = 100
Mary's income = 160
Juan = 140
Juan is then 12.5% less then Mary's income.
I know this approach is wrong because it does not lead to the OA but can you please explain where I made my mistake?
Try plugging in numbers and you will see. If Juan makes $100 and Tim make 40% less than that, then Tim makes $100$40 = $60.
If Tim makes $60 and Juan makes 140% of $60, then Juan makes $84 ($60 + 60*.4) = ($60 + $24) = $84. % don't work the way you were using them.
So, Mary = 160%Tim
Tim = %60Juan
Therefore Mary = %160 (%60 Juan)
1.6 * .6 = .96 = 96%
Answer is C
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I also tried to solve this using following values but could not find the correct answer. Can some one please explain what is the correct value of juan's income of Tim is 100?
Tim's income = 100
Mary's income = 160
Juan = 140
Tim's income = 100
Mary's income = 160
Juan = 140
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If t = 100 and j = Juan's income, let's translate into math the statement Tim's income is 40% less than Juan's income:HPengineer wrote:I also tried to solve this using following values but could not find the correct answer. Can some one please explain what is the correct value of juan's income of Tim is 100?
Tim's income = 100
Mary's income = 160
Juan = 140
100 = j  .4j (100 = Juan's income  40% of Juan's income)
100 = .6j
j = 100/.6 = 1000/6 = 500/3.
Thus, if m = 160, then m/j = 160/(500/3) = 160 * 3/500 = 480/500 = 48/50 = 96/100 = 96%.
Plugging in for Tim's income makes the math messy. This problem requires us to plug and chug: plug in a value for one unknown and use this value to determine the values of all the other unknowns in the problem. When you're plugging and chugging, think about the best place to start plugging in. Since this problem asks what percent of Juan's income is Mary's income, we should let j=100 so that the question becomes: what percent of 100 is Mary's income? This will be an easy question to answer:
j = 100
t = 60 (40% less than Juan's income of 100)
m = 96 (60% more than Tim's income of 60)
So m/j = 96/100 = 96%. So much easier!
The correct answer is C.
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I thought I would share my work on this problem with others who might run into the same issues. I kept getting answer choice E until I worked through what I was doing wrong. Knowing how to translate this question correctly is key to arriving at the right answer. A proper translation of the question also provides insight into what variables you should plug in for.HPengineer wrote:I also tried to solve this using following values but could not find the correct answer. Can some one please explain what is the correct value of juan's income of Tim is 100?
Tim's income = 100
Mary's income = 160
Juan = 140
Previously, I've been told to start with the common element, which is why I initially picked Tim = 100. You can use T = 100 and still arrive at the answer, but it takes longer and may be prone to error.
Let's work on translating the sentences:
"Mary's income is 60% more than Tim's income"
This means M = 1.6T. If the question says X is 60 percent more than Y, then X = 1Y + 0.6Y = 1.6Y
If the question would have said X is 60 percent LESS THAN Y, then X = 1Y  0.6Y = X = 0.4Y
What's key here is not to confuse LESS THAN with PERCENT OF.
60 percent of Y = (60/100)(Y) which reduces to (3/5)(Y)or simply use (0.6)(Y)
60 percent less than Y = 0.4Y
Next the question states
"Tim's income is 40 less than Juan's income."
Again, this means T = 1J  0.4J = 0.6J
Finally, it asks "What percent of Juans income is Mary's income?"
Here's a formation that can be used: What percent of A is B?
This means "Is B" / "Percent of A" x 100
Using this formation: "Is Mary's Income" / "Percent of Juan's Income" or M/J = ?
Although Tim is the common element, you're solving for M/J, and plugging in 100 for J will make the math easier and save you some time.
Let's just say T=100
Then M = 160
Next, T = J  0.4J. Plug in your values: 100 = J  0.4J. 100 = 0.6J. Divide both sides by 0.6. Move the decimals to the right to get 1000/6 = J.
The target question is M/J = 160/(1000/6) = (160*6)/1000 = (16*6)/100 = 96%
That's not terrible, but this could've been much easier if J= 100.
J = 100
T = 60
M = (0.6*60) + 60 = 36+60 = 96
That's it. M=96%
Finally, here's the wrong way to translate the sentences:
"Tims income is 40 less than Juans income."
If T = 100, the translation IS NOT 100 = 0.4J. That is 40 PERCENT OF Juan, NOT 40 percent LESS THAN Juan
Remember, when the question asks for LESS THAN, you are subtracting that percentage from a base of 1 (Ex. x is 2 percent less than y = x = 1y  0.2y = 0.98y)
When the question asks for PERCENT OF, then you are multiplying values: 30% of 70 = (0.3)(70) = 21
I hope this helps!
Poisson wrote:I thought I would share my work on this problem with others who might run into the same issues. I kept getting answer choice E until I worked through what I was doing wrong. Knowing how to translate this question correctly is key to arriving at the right answer. A proper translation of the question also provides insight into what variables you should plug in for.HPengineer wrote:I also tried to solve this using following values but could not find the correct answer. Can some one please explain what is the correct value of juan's income of Tim is 100?
Tim's income = 100
Mary's income = 160
Juan = 140
Previously, I've been told to start with the common element, which is why I initially picked Tim = 100. You can use T = 100 and still arrive at the answer, but it takes longer and may be prone to error.
Let's work on translating the sentences:
"Mary's income is 60% more than Tim's income"
This means M = 1.6T. If the question says X is 60 percent more than Y, then X = 1Y + 0.6Y = 1.6Y
If the question would have said X is 60 percent LESS THAN Y, then X = 1Y  0.6Y = X = 0.4Y
What's key here is not to confuse LESS THAN with PERCENT OF.
60 percent of Y = (60/100)(Y) which reduces to (3/5)(Y)or simply use (0.6)(Y)
60 percent less than Y = 0.4Y
Next the question states
"Tim's income is 40 less than Juan's income."
Again, this means T = 1J  0.4J = 0.6J
Finally, it asks "What percent of Juans income is Mary's income?"
Here's a formation that can be used: What percent of A is B?
This means ("Is B" / "Percent of A") x 100
Using this formation: "Is Mary's Income" / "Percent of Juan's Income" or M/J = ?
Although Tim is the common element, you're solving for M/J, and plugging in 100 for J will make the math easier and save you some time.
Let's just say T=100
Then M = 160
Next, T = J  0.4J. Plug in your values: 100 = J  0.4J. 100 = 0.6J. Divide both sides by 0.6. Move the decimals to the right to get 1000/6 = J.
The target question is M/J = 160/(1000/6) = (160*6)/1000 = (16*6)/100 = 96%
That's not terrible, but this could've been much easier if J= 100.
J = 100
T = 60
M = (0.6*60) + 60 = 36+60 = 96
That's it. M=96%
Finally, here's the wrong way to translate the sentences:
"Tims income is 40 less than Juans income."
If T = 100, the translation IS NOT 100 = 0.4J. That is 40 PERCENT OF Juan, NOT 40 percent LESS THAN Juan
Remember, when the question asks for LESS THAN, you are subtracting that percentage from a base of 1 (Ex. x is 2 percent less than y = x = 1y  0.2y = 0.98y)
When the question asks for PERCENT OF, then you are multiplying values: 30% of 70 = (0.3)(70) = 21
I hope this helps!
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To solve this problem we create variables for the income of Mary, Tim, and Juan, and then set up some equations.ssraf wrote:Marys income is 60% more than Tims income, and Tims income is 40 less than Juans income. What percent of Juans income is Mary's income?
a) 124
b)120
c)96
d)80
e)64
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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I suggest that we choose some nice values that meet the given conditions.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%
Tim's income is 40 percent LESS THAN Juan's income.
Let Juan's income = $100
40% of $100 = $40
This means Tim's income = $100  $40 = $60
Mary's income is 60 percent MORE THAN Tim's income
60% of $60 = $36
So Mary's income = $60+ $36 = $96
What percent of Juan's income is Mary's income?
Juan's income = $100
Mary's income = $96
So, Mary's income is [spoiler]96%[/spoiler] of Juan's income
Answer: C
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