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A certain store sells all maps at one price and all books at another

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Re: A certain store sells all maps at one price and all books at another [#permalink]
Let Selling price of each map be Tk. x and Selling price of each book be Tk. y

12x + 10y = 38, or 6x + 5y = 19 --------------(1)( Dividing by 2)
And 20x + 15y = 60, or 4x + 3y = 12 --------(2) (Dividing by 5)

20 x + 15y = 60(Multiplying eq.2 by 5) -------(3)
18x + 15y = 57(Multiplying eq.1 by 3)---------(4)

(3)-(4) ⫸ 2x = 3
X = 3/2
Putting X = 3/2 in equation no.(1) , 6*(3/2) + 5y = 19
9 + 5y = 19
5y = 10
Y = 2
The price of A map is less than that of a book = 2 – 3/2 = ½ = 0.5(B)
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Re: A certain store sells all maps at one price and all books at another [#permalink]
I may have taken a longer approach, I multiplied the first equation with 3 to make 10b --- 30b and second equation with 2 to make 15b -- 30b.
It made things complicated since it became fractions, however at the end i got 6/4-2/1 = 1/2 --- 0.5\$.
Anyone else took this approach?
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Re: A certain store sells all maps at one price and all books at another [#permalink]
On Monday = 12M + 10B = 38 ...........(1)

On Tuesday = 20M + 15B = 60 ...........(2)
Now, we need to find the difference between the price of a map and a book, which is given by (B - M).

Multiply equation (1) by 2:
2(12M) + 2(10B) = 2(38)
24M + 20B = 76 ...........(3)

Now, subtract equation (2) from equation (3) to eliminate the B variable:
(24M + 20B) - (20M + 15B) = 76 - 60
4M + 5B = 16

Now we have a system of two equations:
12M + 10B = 38 ...........(1)
4M + 5B = 16 ...........(4)

From equation (4), we can express B in terms of M:
5B = 16 - 4M
B = (16 - 4M)/5

Now substitute this value of B into equation (1):
12M + 10((16 - 4M)/5) = 38

12M + 2(16 - 4M) = 38
12M + 32 - 8M = 38
4M = 38 - 32
4M = 6
M = 6/4
M = 1.50

the value of M =1.50 ,let's find the value of B (price of a book) using equation (4):
B = (16 - 4M)/5
B = (16 - 4(1.50))/5
B = (16 - 6)/5t
B = 10/5
B = 2.00

Now difference between the price of a map and a book: (B - M)
2.00 - 1.50 = 0.50
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Re: A certain store sells all maps at one price and all books at another [#permalink]
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Bunuel wrote:
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) \$l.25

If each map sells for m and each book sells for b, we have:

b – m = ?

12m + 10b = 38
20m + 15b = 60

If we multiply the first equation by 3 and the second equation by 2, we have:

36m + 30b = 114
40m + 30b = 120

If we subtract the first equation from the second, we have:

4m = 6

m = 3/2, which we can substitute into the first equation:

12(3/2) + 10b = 38

10b = 20

b = 2 and therefore b – m = 2 – 1.5 = 0.5