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# GMAT: Math 29

148-153, pgs. 172-173. Created by Sal Khan.

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• For problem #153 at , are we sure the answer is D, 23 years old? I don't have the book so I don't know the other possible answers, but here's how I solved it:

J = B + 14 and J + 10 = 2(J - 14) + 10 because B = J - 14. This turns into J = 2J - 28 which turns into J = 28, so J + 5 = 33 years old. What Sal did was combine the -14 and 10 into -4, but I thought we used order of operations to solve inside the parenthesis first, thus leaving 10 outside the parenthesis to be added later. I also solved the problem a different way and got the same answer, 33. • You can double check your answer thinking about the question logically. If Jack is 33 years old in five years then he is currently 28 years old. The problem begins with the statement: Jack is 14 years older than Bill. This means that Bill would have to be 14 years old (If Jack is 14 years older than Bill and Jack is 28 this means Bill’s age is 14). Already you should see the error here, because Jack is already double Bills age if this condition were true. You can further verify this issue by looking at the second statement in the problem. It states that in ten years Jack will be twice as old as Bill. If you add ten years to both Jack and Bill you get 38 (28 +10) and 24 (14+10) for their ages respectively. Clearly, 38 is not 24 x 2.

You can also verify Sal’s answer with the same logical process. If in five years Jack is 23 years old then it means his current age is 18. Looking at the first statement of the problem, it is understood that if Jack is 18 years old then Bill is 4 years old (J = B +14). The second statement says that Jack will be twice as old as Bill in 10 years. If you add ten years to each individual, Jack is 28 years old and Bill is now 14 years old. Since 28 is twice the amount of 14, you know Sal’s answer of 23 is correct.
• 153) at , Why does Hal set it as J+10 = 2(B+10)? In my head, it should be J+10 = 2B +10.

In my head, Jack in 10 years, is twice as old as Bill is, in 10 years. Jack in 10 years, is not twice as old as Bill is in 20 years...no? • In these problems, you have to think about what time in past or future you are talking about for each clue.
Maybe it would help to look at it this way:
What are their relative ages `now`?
Jack is some age that is 14 years older than Bill
We call Jack's age `now` as J and Bill's age `now` as B
So if Jack is 20, Bill is 6

That is why we say that J = B + 14
OK, so to the heart of your question:
How old will Jack be in 10 years? The actual wording seems to have been, "If `in 10 years`, Jack will be twice as old as Bill"... Now we have to look ahead to `the future in 10 years`:
Jack will be J + 10
How old will Bill be in 10 years?
B + 10
So at that point in the future, Jack will be twice Bill's age. If it meant that Jack WILL be twice Bill's age now, the wording would have specified now.
Now you can set up the equation for `that point in the future`.
J + 10 = 2 (B + 10)
We need a single variable to solve, so we can use the B = J - 14. No matter what age Jack is, Bill will remain 14 years behind, so you can use that as a constant difference.
which gives us
J + 10 = 2 ( J - 14 + 10)
J + 10 = 2 ( J - 4)
J + 10 = 2J - 8, leading to J = 18

In this problem, there is the additional challenge of asking about a 3rd point in time, which is 5 years from now. So then you have to use Jack's age now and add 5 years.

Practice with these age problems helps you remember to look for the time cues.
• q.151 why you multiblied the two percentages ?? i think you should add the additional discount to the first one, so the total discount will be 65% because you said the additional discount is of the original price
(1 vote) • Could you tell me what this is
10=∆+8
(1 vote) • I looked through the whole video a second time to find where this was mentioned, but maybe you were just curious.
Δ is usually used to mean change, especially having to do with graphs or even just values. An example is Δy means `change in the y value` between two points.
So in that case, the meaning of your equation might be
10 = change in a value + 8
So, what number plus 8 equals 10? Δ must equal 2.

Or, you might be doing some pictorial math. Then you would need to find
10 equals Δ + 8
What value, when added to 8 would equal 10. Δ = 2
Or, you can just use algebra:
10 = ∆ + 8; subtract 8 from both sides:
10 -8 = ∆ + 8 - 8
2 = ∆
(1 vote)
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(1 vote) 