PS- map sell problem

[madsport]

A certain store sells all maps at one price and all books at another price. On Monday the store sold 12 maps and 10 books for a total of $38.00, and on Tuesday the store sold 20 maps and 15 books for a total of $60.00. At this store, how much less does a map sell for than a book?

(A) $0.25
(B) $0.50
(C) $0.75
(D) $1.00
(E) $1.25

The answer is B

Can someone post a quick way of solving this problem?

[niraj_a]

i used simultaneous equations and was able to solve this under 2 mins.....

[madsport]

I would love to see the steps taken to solve this one.

[cramya]

Hi Madsport,


Let x be the price of the map and y be the price of the book.

12x+10y = 38 Eq 1
20x+15y = 60 Eq 2

Divide Eq1 by 2 to reduce it further and Eq2 by 5

6x+5y = 19
4x+3y = 12

Solve we get y = 2 x = 3/2 = 1.5

There y-x is .50. The map sells for $0.50 less than a book

[gmataug08]

two equations formed would be

12m + 10b = 38

20m + 15b = 60 ->(dividing by 5) -> 4m + 3b = 12 ->(multiplying by 3, we get ) -> 12m + 9b = 36

solving the two equations 12m + 10b = 38 & 12m + 9b = 36

we get b= 2 ; on substituting we get m = 3/2 -> 1.5

hence the answer is B .

[alescau]

12x+10y = 38 Eq 1
20x+15y = 60 Eq 2

a step for speed would be to multiply Eq 1 by 1.5 and then subtract Eq 2 to eliminate y.

[abcdefg]

I have these two equations:

1. 6x+5y=19
2. 4x+3y=12.

A. Steps 1-2 = 2x+2y = 7.
B. 2(x+y) = 7.
C. (x+y) = 7/2 = 3.5
D. I just randomly picked x = 1, y = 2.5.
E. 2.5 - 1 = 1.5. But that's not the answer!

Can someone help point out what I did wrong? thanks.