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A breakfast that consists of 1 ounce of corn puffs and 8

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chintzzz
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A breakfast that consists of 1 ounce of corn puffs and 8 [#permalink] New post   19 Jun 2010, 01:14
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A breakfast that consists of 1 ounce of corn puffs and 8 ounces of fruit X provides 257 calories. When 8 ounces of Fruit Y is substituted for the 8 ounces of fruit X, the total number of calories is reduced to 185. If fruit X provides 1.8 times as many calories as fruit Y, how many calories does 8 ounces of fruit Y alone provide?

A. 11.25
B. 72
C. 90
D. 95
E. 129.6
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C
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vinay.kaipra
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Re: need assistance with resolving this problem question.. [#permalink] New post   19 Jun 2010, 01:24
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Let me try to explain the how I reached the answer.

As per the first statement, 1 CP + 8 FX = 257C (CP Corn puffs, FX Fruit X, C Calories).
As per the second statement, 1CP + 8FY = 185C (FY Fruit Y)

Now, if we subtract 1st equation with second one,
8FX - 8FY = (257 - 185) C
8(FX-FY) = 72C

Now, as per the 3rd statement, FX = 1.8FY
Hence, 8 (1.8 FY - FY) = 72C
8(.8FY) = 72C
8 FY = 72/0.8 C = 90 C.

Thanks.
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A breakfast that consists of 1 ounce of corn puffs and 8 [#permalink] New post   19 Jun 2010, 01:41
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Quote:
A breakfast that consists of 1 ounce of corn puffs and 8 ounces of fruit X provides 257 calories. When 8 ounces of Fruit Y is substituted for the 8 ounces of fruit X, the total number of calories is reduced to 185. If fruit X provides 1.8 times as many calories as fruit Y, how many calories does 8 ounces of fruit Y alone provide?

(A) 11.25
(B) 72
(C) 90
(D) 95
(E) 129.6


Let the number of calories in 1 ounce of corn be \(c\), in 1 ounce of fruit X be \(x\) and 1 ounce of fruit Y be \(y\).

Given:
    (1) \(c+8x=257\);
    (2) \(c+8y=185\);
    (3) \(x=1.8y\).


Question:
    \(8y=?\)

Subtract (2) from (1):
    \(c+8x-c-8y=257-185\);
    \(8x-8y=72\).

Since \(x=1.8y\), then:
    \(8*1.8y-8y=72\);
    \(0.8*8y=72\);
    \(8y=90\).

Answer: C.
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Re: need assistance with resolving this problem question.. [#permalink] New post   19 Jun 2010, 01:44
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Here's my 15 sec solution

Difference in total calories o both meals = 72 (is same as difference in calories provided by fruit X and Y)
if X provides 1.8 times calories than Y. It means X provides 80% more calories than Y
Now just pick number number and see 72 is 80% of which option (easy pick C)
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Re: need assistance with resolving this problem question.. [#permalink] New post   19 Jun 2010, 02:29
thanks a lot...i realised that i made a careless mistake on this
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Re: A breakfast that consists of 1 ounce of corn puffs and 8 [#permalink] New post   04 Aug 2014, 19:28
Three equations are created from given information

c + 8x = 257 .......... (1)

c + 8y = 185 ........... (2)

x = 1.8y ............... (3)

(1) - (2)

8x - 8y = 72

8(1.8y) - 8y = 72

8y(1.8-1) = 72

\(8y = \frac{72}{0.8} = 90\)

Answer = C
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Re: A breakfast that consists of 1 ounce of corn puffs and 8 [#permalink] New post   04 Aug 2014, 20:47
1C + 8Fx = 257
1C + 8Fy = 185

8( Fx - Fy ) = 72

8( 1.8Fy - Fy ) = 72

8Fy = 72/0.8 = 90
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Re: A breakfast that consists of 1 ounce of corn puffs and 8 [#permalink] New post   28 Jan 2015, 04:15
c + 8x = 257 .......... (a)

c + 8y = 185 ........... (b)

x = 1.8y ............... (3)

Solving we get y = 11.25...9y = 90
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Re: A breakfast that consists of 1 ounce of corn puffs and 8 [#permalink] New post   04 Mar 2020, 08:25
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chintzzz wrote:
A breakfast that consists of 1 ounce of corn puffs and 8 ounces of fruit X provides 257 calories. When 8 ounces of Fruit Y is substituted for the 8 ounces of fruit X, the total number of calories is reduced to 185. If fruit X provides 1.8 times as many calories as fruit Y, how many calories does 8 ounces of fruit Y alone provide?

A. 11.25
B. 72
C. 90
D. 95
E. 129.6


We see that 8 ounces of fruit X has 257 - 185 = 72 calories more than 8 ounces of fruit Y. Since fruit X provides 1.8 times as many calories as fruit Y, we can create the equations:

X = Y + 72

and

X = 1.8Y

Therefore, we have:

Y + 72 = 1.8Y

72 = 0.8Y

90 = Y

Answer: C
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Re: A breakfast that consists of 1 ounce of corn puffs and 8 [#permalink] New post   05 Mar 2020, 06:23
let us consider one ounce of puff as o, 8 ounce of fruit x as 8x and 8 ounce of fruit y as 8y . now we get o + 8x=257 and
o+8y=185 . also we have x=1.8y .solving these three equation we get y and multiplying it with 8 we get 8y=90 which is required answer.
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Re: A breakfast that consists of 1 ounce of corn puffs and 8 [#permalink] New post   21 Apr 2024, 13:28
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