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Joseph bought nails for $0.01 each, hooks for $0.02 each, and screws 26 Dec 2019, 02:07
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B
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72% (02:39) correct 28% (03:07) wrong based on 58 sessions

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Joseph bought nails for $0.01 each, hooks for $0.02 each, and screws for $0.03 each. He bought a total of 18 items and paid a total of $0.32. If he bought twice as many nails as screws, how many hooks did he buy?

(A) 4
(B) 6
(C) 7
(D) 8
(e) 10
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B
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Joseph bought nails for $0.01 each, hooks for $0.02 each, and screws 26 Dec 2019, 09:19
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Nail = n x $0.01 = 2s x $0.01
Hook = h x $0.02,
Screws = s x $0.03.

2s + h + s = 18 --> h=3(6-s)

So, h must be multiple of 3. The only sensible option is (B) : h=6 and consequently, s=4 and n=2s=8

Check:
*h+s+n=18 (OK!)
*8*1¢ + 6*2¢ + 4*3¢ = 32¢ (OK!)

FINAL ANSWER IS (B)

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Joseph bought nails for $0.01 each, hooks for $0.02 each, and screws 26 Dec 2019, 04:15
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given
x+y+z=18
and
x+2y+3z=32
also x=2z
we can solve for y
as z=18-y/3
so
5z+2y=32
y = 6
IMOB


Joseph bought nails for $0.01 each, hooks for $0.02 each, and screws for $0.03 each. He bought a total of 18 items and paid a total of $0.32. If he bought twice as many nails as screws, how many hooks did he buy?

(A) 4
(B) 6
(C) 7
(D) 8
(e) 10
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Joseph bought nails for $0.01 each, hooks for $0.02 each, and screws 26 Dec 2019, 07:55
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Quote:

Joseph bought nails for $0.01 each, hooks for $0.02 each, and screws for $0.03 each. He bought a total of 18 items and paid a total of $0.32. If he bought twice as many nails as screws, how many hooks did he buy?

(A) 4
(B) 6
(C) 7
(D) 8
(e) 10
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n=2s
n+h+s=18, h=18-3s
n+2h+3s=32, 2h+5s=32, 36-6s+5s=32, -s=-4, s=4
h=18-12=6

Ans (B)
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Joseph bought nails for $0.01 each, hooks for $0.02 each, and screws 26 Dec 2019, 10:49
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Joseph bought nails for $0.01 each, hooks for $0.02 each, and screws for $0.03 each. He bought a total of 18 items and paid a total of $0.32. If he bought twice as many nails as screws, how many hooks did he buy?

(A) 4
(B) 6
(C) 7
(D) 8
(e) 10

Let N be the number of nails, S be the number of Screws and H be the number of hooks.
N + S + H = 18 and 0.01*N + 0.02*H + 0.03*S = 0.32
Also N = 2S
So, 3S + H = 18
Possible solutions of 3S + H = 18 are
3 + 15 = 18
6 + 12 = 18
9 + 9 = 18
12 + 6 = 18
15 + 3 = 18

Only the highlighted set satisfies the condition since N, S and H all are positive integers. Also, seeing the options only B satisfies the conditions.
Cross verifying 0.01*8 + 0.02*6 + 0.03*4 = 0.32 satisfies.

Answer B.
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Joseph bought nails for $0.01 each, hooks for $0.02 each, and screws 26 Dec 2019, 12:17
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Quote:
Joseph bought nails for $0.01 each, hooks for $0.02 each, and screws for $0.03 each. He bought a total of 18 items and paid a total of $0.32. If he bought twice as many nails as screws, how many hooks did he buy?

(A) 4
(B) 6
(C) 7
(D) 8
(e) 10
Show more

The number of screws: x
Because Joseph bought twice as many nails as screws => The number of nails: 2x
The number of hooks: y

=> 0.01*2*x + 0.02*y + 0.03*x = 0.32
=> 5x + 2y = 32 (1)
meanwhile: x + 2x +y = 18
=> 3x + y = 18 (2)

From (1)&(2) => x=4; y=6
=> the number of hooks = 6

Choice B
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Joseph bought nails for $0.01 each, hooks for $0.02 each, and screws 26 Dec 2019, 20:46
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Cost per nail = 0.01, cost per hook=0.02, and cost per screw=0.03. Total cost=0.32, and total items bought=18. We are informed that Joseph bought twice as many screws as nails.
Possible combinations: 2 screws, 4 nails, and 14 hooks; 3 screws, 6 nails, and 9 hooks; 4 screws, 8 nails, and 6 hooks; 5 screws, 10 nails, and 3 hooks.
Looking at the answer choices, the only possible combination is 4 screws, 8 nails, and 6 hooks.
Checking to confirm the total cost involved: 4(0.03)+8(0.01)+6(0.02)=0.12+0.08+0.12=0.32.
Hence the number of hooks that Joseph bought is 6.

The answer is B.
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Joseph bought nails for $0.01 each, hooks for $0.02 each, and screws 28 Dec 2019, 07:23
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Joseph bought nails for $0.01 each, hooks for $0.02 each, and screws for $0.03 each. He bought a total of 18 items and paid a total of $0.32. If he bought twice as many nails as screws, how many hooks did he buy?


Nails (N) are twice Screws (S), so:

N S $
2 1 0,05
4 2 0,10
6 3 0,15
8 4 0,20
10 5 0,25

Total is N + H + S = 18 units = 0,32

(always start middle, so you can work your way down/up)

N + S = $ H (18 - N - S) = $ Total
6 3 = 0,15 9 ( 18 - 6 - 3) = 0,18 $0,33 X
8 4 = 0,20 6 = 0,12 $0,32 V
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