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Math Expert V
Joined: 02 Sep 2009
Posts: 61403
A certain store sells all maps at one price and all books at another  [#permalink]

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Difficulty:   15% (low)

Question Stats: 86% (02:28) correct 14% (03:09) wrong based on 134 sessions

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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

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Director  G
Joined: 20 Feb 2015
Posts: 724
Concentration: Strategy, General Management
Re: A certain store sells all maps at one price and all books at another  [#permalink]

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

multiply eq 1 by 5 and eq 2 by 3

60x+50y=38*5
60x+45y=60*3

subtracting 1 from 2

5y=190-180
y=2

therefore
x=18/12=1.5

difference in price =0.5
Retired Moderator P
Joined: 19 Mar 2014
Posts: 912
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: A certain store sells all maps at one price and all books at another  [#permalink]

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Let M = Number Of Maps
Let B = Number of Books

Based on the Question we can create below two Equations:

12M + 10B = 38 ------------- Eq.1
20M + 15B = 60 ------------- Eq.2

Multiply Eq. 1 By 5
Multiply Eq.2 By 3

60M + 50B = 190
60M + 45B = 180

Subtracting these two equations we get:

5B = 10

B = 2

Put this value of B in any of the equation, for the solution we will take Eq. No. 1

12M + 10B = 38 ------------- Eq.1

12M + 10*2 = 38

12M = 38 - 20

12M = 18

M = 18/12 = 3/2 = 1.5

We are asked, value of B - M

B - M = ?

2 - 1.5 = 0.5

Hence, the answer is (B) \$0.50

Regards,
YM
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"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

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Manager  B
Joined: 14 Sep 2019
Posts: 172
Re: A certain store sells all maps at one price and all books at another  [#permalink]

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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) Re: A certain store sells all maps at one price and all books at another   [#permalink] 25 Jan 2020, 21:42
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