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# A stationery shop sold pencils for \$0.70 each and erasers for \$0.50 ea

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
A stationery shop sold pencils for \$0.70 each and erasers for \$0.50 ea  [#permalink]

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03 Oct 2018, 23:31
1
00:00

Difficulty:

25% (medium)

Question Stats:

78% (01:44) correct 22% (02:22) wrong based on 32 sessions

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A stationery shop sold pencils for \$0.70 each and erasers for \$0.50 each. If a girl purchased both pencils and erasers from the shop for a total of \$6.30, what is the total number of pencils and erasers the girl purchased? The girl purchased at least one of both the items.

(A) 9
(B) 10
(C) 11
(D) 12
(E) 13

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Re: A stationery shop sold pencils for \$0.70 each and erasers for \$0.50 ea  [#permalink]

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03 Oct 2018, 23:49
Bunuel wrote:
A stationery shop sold pencils for \$0.70 each and erasers for \$0.50 each. If a girl purchased both pencils and erasers from the shop for a total of \$6.30, what is the total number of pencils and erasers the girl purchased? The girl purchased at least one of both the items.

(A) 9
(B) 10
(C) 11
(D) 12
(E) 13

0.7p + 0.5e = 6.3

i.e. 7p + 5e = 63

p = 9 and e = 0 is one solution
p = 4 and e = 7 is another solution i.e. minimum sum = 4+7 = 11

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Re: A stationery shop sold pencils for \$0.70 each and erasers for \$0.50 ea  [#permalink]

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04 Oct 2018, 01:22
1
Bunuel wrote:
A stationery shop sold pencils for \$0.70 each and erasers for \$0.50 each. If a girl purchased both pencils and erasers from the shop for a total of \$6.30, what is the total number of pencils and erasers the girl purchased? The girl purchased at least one of both the items.

(A) 9
(B) 10
(C) 11
(D) 12
(E) 13

6.30 = 0.7p + 0.5e

Multiplty by 10 to make it easier to deal with.

63 = 7p + 5e

63 is divisible by 7

9 = p + (5e)/7
p = 9 - (5e)/7

erasers must be a multiple of 7.

e = 7
P = 9 - (5*7)/7 = 9-5 = 4

P+E = 11

7 * 5 = 35
4 * 7 = 28

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Posts: 8895
Location: Pune, India
Re: A stationery shop sold pencils for \$0.70 each and erasers for \$0.50 ea  [#permalink]

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04 Oct 2018, 01:44
Bunuel wrote:
A stationery shop sold pencils for \$0.70 each and erasers for \$0.50 each. If a girl purchased both pencils and erasers from the shop for a total of \$6.30, what is the total number of pencils and erasers the girl purchased? The girl purchased at least one of both the items.

(A) 9
(B) 10
(C) 11
(D) 12
(E) 13

Use integer solutions in two variables to get the answer:

.70P + .50E = 6.30

7P + 5E = 63

We immediately see the first solution since 63 is a multiple of 7.
So P = 9 and E = 0 will be the first solution. Since she buys both pencils and erasers, so this is not our answer.

We know the next solution will be obtained by decreasing P by 5 (co-efficient of E) and increasing E by 7 (co-efficient of P). So next solution is P = 4, E = 7. Total number of items = 4+7 = 11
Check this post for more on this method: https://www.veritasprep.com/blog/2011/0 ... -of-thumb/
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Re: A stationery shop sold pencils for \$0.70 each and erasers for \$0.50 ea   [#permalink] 04 Oct 2018, 01:44
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