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help needed on word problem

by sohaib_iba » Wed Feb 24, 2010 7:16 am
Ellen paid $11.80 for 40 postage stamps. If some of the stamps were 33-cent stamps and the rest were 23-cent stamps, how many 33-cent stamps did she buy?

A) 13
B) 17
C) 22
D) 25
E) 26

Please help me at this question as i am unable to solve it yet. Thanks in advance
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by ldoolitt » Wed Feb 24, 2010 7:39 am
sohaib_iba wrote:Ellen paid $11.80 for 40 postage stamps. If some of the stamps were 33-cent stamps and the rest were 23-cent stamps, how many 33-cent stamps did she buy?

A) 13
B) 17
C) 22
D) 25
E) 26

Please help me at this question as i am unable to solve it yet. Thanks in advance
I get 26.

The question stem screams EQUATIONS. And this stem gives you two. First set up your variables

X = quantity of 33 cent postage stamps (your answer)
Y = quantity of 23 cent postage stamps

(1) X+Y = 40 (since you have 40 total stamps)
(2) .33*X + .23*Y = 11.80 (since you paid 11.80 for all the stamps)

Take (2) and multiply through by 100 to clear out the decimals

33*X + 23*Y = 1180

Take (1) and multiply through by -23

-23*X - 23*Y = 40*-23

Add these two together. Skipping the arithmetic involved in canceling the Y's:

10*X = 1180 - 40*23
X = 118 - 4*23
X = 26
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by Pedros » Wed Feb 24, 2010 7:43 am
+1 for 26

0.33x + 0.23y = 11.80

x+y = 40 so y = 40-x

0.33x + 0.23 ( 40 -x) = 11.8

0.1 x = 2.6

x = 26
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