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12 Jan 2026, 09:57
Kudos
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A shopkeeper at a movie theater concession stand mixes almonds and pistachios in a ratio of 6:5 by weight. The mixture is then sold at $25 per pound, earning a 25% profit. If the cost of almonds for the shopkeeper is $11 more per pound than the cost of pistachios, what is the cost price of almonds per pound?
A. $14
B. $20
C. $25
D. $26
E. $29
A. $14
B. $20
C. $25
D. $26
E. $29
12 Jan 2026, 09:57
Kudos
Bookmarks
Official Solution:
A shopkeeper at a movie theater concession stand mixes almonds and pistachios in a ratio of 6:5 by weight. The mixture is then sold at $25 per pound, earning a 25% profit. If the cost of almonds for the shopkeeper is $11 more per pound than the cost of pistachios, what is the cost price of almonds per pound?
A. $14
B. $20
C. $25
D. $26
E. $29
Assume the total weight of the mixture is 11 pounds. This simplifies the math because the total weight 11 pounds matches the sum of the ratio 6 parts almonds + 5 parts pistachios.
• Almonds: 6 parts of the 11-pound mixture = 6 pounds of almonds.
• Pistachios: 5 parts of the 11-pound mixture = 5 pounds of pistachios.
Let the cost of pistachios per pound be \(p\). Then, the cost of almonds per pound is \(p + 11\).
Thus, the total cost of the 11-pound mixture is:
\(6(p + 11) + 5p\)
The selling price of the mixture is 25 dollars per pound, and the shopkeeper earns a 25% profit. So the cost price of the mixture is \(\frac{25}{1.25} = 20\) dollars per pound, and 20 * 11 for 11 pounds.
So, we get:
\(6(p + 11) + 5p = 20 * 11\)
\(p = 14\)
So, the cost of pistachios is 14 dollars per pound, and the cost of almonds is \(p + 11 = 14 + 11 = 25\) dollars per pound.
Answer: C
A shopkeeper at a movie theater concession stand mixes almonds and pistachios in a ratio of 6:5 by weight. The mixture is then sold at $25 per pound, earning a 25% profit. If the cost of almonds for the shopkeeper is $11 more per pound than the cost of pistachios, what is the cost price of almonds per pound?
A. $14
B. $20
C. $25
D. $26
E. $29
Assume the total weight of the mixture is 11 pounds. This simplifies the math because the total weight 11 pounds matches the sum of the ratio 6 parts almonds + 5 parts pistachios.
• Almonds: 6 parts of the 11-pound mixture = 6 pounds of almonds.
• Pistachios: 5 parts of the 11-pound mixture = 5 pounds of pistachios.
Let the cost of pistachios per pound be \(p\). Then, the cost of almonds per pound is \(p + 11\).
Thus, the total cost of the 11-pound mixture is:
\(6(p + 11) + 5p\)
The selling price of the mixture is 25 dollars per pound, and the shopkeeper earns a 25% profit. So the cost price of the mixture is \(\frac{25}{1.25} = 20\) dollars per pound, and 20 * 11 for 11 pounds.
So, we get:
\(6(p + 11) + 5p = 20 * 11\)
\(p = 14\)
So, the cost of pistachios is 14 dollars per pound, and the cost of almonds is \(p + 11 = 14 + 11 = 25\) dollars per pound.
Answer: C
17 Apr 2026, 02:54
Kudos
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This becomes very simple using mixtures and alligations. Although I made a small mistake here.
So the Cp is 25*4/5 = 20
This becomes centre of the alligation, eventual price and we have the final ratios as 6:5.
We need to be careful that Almond is 11+Pistachios and thus we subtraction greater - smaller giving us 5.
Or A-20 = 5. A = 25.
P = 14.
Mistake I did:
Took 20-A = 5 and got 15 for almonds and 26 for pistachios, accidentally flipping the ratios and chose 26 as answer.
Need to always be careful with which ratios are taken.
Great option that makes the questions quite tricky!
So the Cp is 25*4/5 = 20
This becomes centre of the alligation, eventual price and we have the final ratios as 6:5.
We need to be careful that Almond is 11+Pistachios and thus we subtraction greater - smaller giving us 5.
Or A-20 = 5. A = 25.
P = 14.
Mistake I did:
Took 20-A = 5 and got 15 for almonds and 26 for pistachios, accidentally flipping the ratios and chose 26 as answer.
Need to always be careful with which ratios are taken.
Great option that makes the questions quite tricky!
Bunuel
