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If a grocer mixes 5 pounds of egg noodles costing $0.80 per pound with

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Bunuel
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If a grocer mixes 5 pounds of egg noodles costing $0.80 per pound with [#permalink] New post   18 Jan 2017, 11:29
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If a grocer mixes 5 pounds of egg noodles costing $0.80 per pound with 2 pounds of spinach noodles costing $1.50 per pound, what will be the cost per pound of the new mixture be?

A. $1.00
B. $1.15
C. $1.30
D. $1.45
E. $7.00
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Re: If a grocer mixes 5 pounds of egg noodles costing $0.80 per pound with [#permalink] New post   18 Jan 2017, 14:10
\(\frac{(5 * 0.80 + 2 * 1.50)}{( 5 + 2)}\) = \(\frac{(4 + 3)}{7}\) = $1.00

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Re: If a grocer mixes 5 pounds of egg noodles costing $0.80 per pound with [#permalink] New post   18 Jan 2017, 18:49
Bunuel wrote:
If a grocer mixes 5 pounds of egg noodles costing $0.80 per pound with 2 pounds of spinach noodles costing $1.50 per pound, what will be the cost per pound of the new mixture be?

A. $1.00
B. $1.15
C. $1.30
D. $1.45
E. $7.00


weight * cost of egg noodles + weight * cost of spinal noodles = 5*0.8 + 2*1.5 = 4+ 3 = 7

The new mixtures weight is combination of weight of egg + spinach, equals = 7 pounds which costs $7.

Cost per pound = $7/7 = $1 ANS :A
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Re: If a grocer mixes 5 pounds of egg noodles costing $0.80 per pound with [#permalink] New post   18 Jan 2017, 20:03
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Bunuel wrote:
If a grocer mixes 5 pounds of egg noodles costing $0.80 per pound with 2 pounds of spinach noodles costing $1.50 per pound, what will be the cost per pound of the new mixture be?

A. $1.00
B. $1.15
C. $1.30
D. $1.45
E. $7.00


Hi,

Two ways..
1) exactly the way done above
Total weight/ total quantity= \(\frac{5*0.8+2*1.5}{2+5}\)=7/7=1

2) weighted average method.
This method is very helpful in simplifying otherwise complicated Qs..
The difference in two quantities is to be divided in weight proportional...

Here the qty of 0.8 is more , so answer will be closer to it..
Ans = \(\frac{2}{2+5}*(1.5-0.8)+0.8=\frac{2}{7}*0.7+0.8=0.2+0.8=1\)
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Re: If a grocer mixes 5 pounds of egg noodles costing $0.80 per pound with [#permalink] New post   19 Jan 2017, 04:55
Bunuel wrote:
If a grocer mixes 5 pounds of egg noodles costing $0.80 per pound with 2 pounds of spinach noodles costing $1.50 per pound, what will be the cost per pound of the new mixture be?

A. $1.00
B. $1.15
C. $1.30
D. $1.45
E. $7.00



Another way is based on reasoning:

If we have equal quantities (whatever the quantity is) of both ingredients, the average price will be in exactly in middle of $0.8 & $1.5. i.e it will be $1.15.

Since we have more quantity of least expensive ingredient (egg noodles), the price will tend to lower than $1.15. There is only one answer.

Answer: A
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Re: If a grocer mixes 5 pounds of egg noodles costing $0.80 per pound with [#permalink] New post   20 Jan 2017, 00:13
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Hi,

This is a perfect question where we can make use of the alligation/mixture diagram. Please go through the below link to get a sense on how the alligation/mixture diagram can be used.

https://gmatclub.com/forum/a-snack-mix-that-is-20-raisins-is-blended-with-a-second-mix-that-is-232402.html#p1791639

Now creating the alligation diagram for the cost price of egg noodles and spinach noodles (values associated with the word per) we get

Attachment:
Mixtures 3.png
Mixtures 3.png [ 6.63 KiB | Viewed 3214 times ]


Now subtracting along the diagonals

1.5 - x = 5
x - 0.8 = 2

Cross multiplying we get

3 - 2x = 5x - 4 ------> 7x = 7 -----> x = 1

Answer : A
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Re: If a grocer mixes 5 pounds of egg noodles costing $0.80 per pound with [#permalink]
20 Jan 2017, 00:13
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