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Joe has a collection of 23 coins, consisting of 5-cent coins, 10-cent
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29 Mar 2019, 11:30
29 Mar 2019, 11:30
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Difficulty:
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Question Stats:
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Joe has a collection of 23 coins, consisting of 5-cent coins, 10-cent coins, and 25-cent coins. He has 3 more 10-cent coins than 5-cent coins, and the total value of his collection is 320 cents. How many more 25-cent coins does Joe have than 5-cent coins?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Re: Joe has a collection of 23 coins, consisting of 5-cent coins, 10-cent
[#permalink]
30 Mar 2019, 00:16
30 Mar 2019, 00:16
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Expert Reply
Noshad wrote:
Joe has a collection of 23 coins, consisting of 5-cent coins, 10-cent coins, and 25-cent coins. He has 3 more 10-cent coins than 5-cent coins, and the total value of his collection is 320 cents. How many more 25-cent coins does Joe have than 5-cent coins?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
We can form three equations to solve ..
Let the number of 5-cent coins, 10-cent coins, and 25-cent coins be x, y and z.
I) Joe has a collection of 23 coins - x+y+z=23
II) He has 3 more 10-cent coins than 5-cent coins - y=x+3
III) the total value of his collection is 320 cents - 5x+10y+25z=320 or x+2y=5z=64...
substitute y =x+3..
I) x+x+3+z=23....2x+z=20.....z=20-2x
substitute the values in (III)
x+2(x+3)+5(20-2x)=64.......x+2x+6+100-10x=64......7x=106-64.....7x=42....x=6
therefore z=20-2*6=8..
Thus z-x=8-6=2
C
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Re: Joe has a collection of 23 coins, consisting of 5-cent coins, 10-cent
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30 Mar 2019, 01:41
30 Mar 2019, 01:41
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Noshad wrote:
Joe has a collection of 23 coins, consisting of 5-cent coins, 10-cent coins, and 25-cent coins. He has 3 more 10-cent coins than 5-cent coins, and the total value of his collection is 320 cents. How many more 25-cent coins does Joe have than 5-cent coins?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
slightly lengthy question as it involves too much of substitution
given
x+y+x=23
x+3=y
need to find z-x value
5x+10y+25z=320
x+2y+5z=64
also 2x+z=20
z=20-2x
x+2y+100-10x=64
x+2*(x+3)+5(20-2x)=64
solve x= 6
so z= 20-12 ; 8
x-z ; 2
IMO C
