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Mike has twice as many stamps as Jean has. After he gives

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Mike has twice as many stamps as Jean has. After he gives

by BTGmoderatorDC » Thu May 30, 2019 11:22 pm

00:00

A

B

C

D

E

Global Stats

Mike has twice as many stamps as Jean has. After he gives Jean 6 stamps, he still has 8 more stamps than Jean does. How many stamps did Mike have originally?

A. 28
B. 32
C. 36
D. 38
E. 40

OA E

Source: Princeton Review

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by ceilidh.erickson » Sat Jun 01, 2019 10:45 am
We can easily translate this algebraically. Let M = Mike's original # of stamps, and J - Jean's original # of stamps.

Mike has twice as many stamps as Jean has -->
$$M=2J$$

After he gives Jean 6 stamps, he still has 8 more stamps than Jean does -->
$$M-6=(J+6)+8$$
*NB: remember that in an EXCHANGE problem, when he gives her 6 stamps, he loses 6 stamps (M-6) but she also gains 6 stamps (J+6).

Now simplify the 2nd equation:
$$M-6=(J+6)+8$$
$$M-6=J+14$$
$$J=M-20$$

Now substitute this in for J in the 1st equation to solve for M:
$$M=2J$$
$$M=2(M-20)$$
$$M=2M-40)$$
$$M=40$$

Ceilidh Erickson
EdM in Mind, Brain, and Education

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by ceilidh.erickson » Sat Jun 01, 2019 10:51 am
This type of 2-variable word problem is know as an EXCHANGE problem, and it can be tricky. For more on exchange problems and translating other tricky word problems, here is a video lesson: