Shannon bought 9 pounds of almonds for a total cost of $27. The cost per pound of cashews is 70% more than the cost of almonds. Shannon bought enough cashews that when she mixed them with the almonds the cost was $4.00 per pound. What percent of the mixture by weight was almonds?

Question

Shannon bought 9 pounds of almonds for a total cost of $27. The cost per pound of cashews is 70% more than the cost of almonds. Shannon bought enough cashews that when she mixed them with the almonds the cost was $4.00 per pound. What percent of the mixture by weight was almonds?

I couldn't get far into the problem because when I do 4 x .70 I get a number for the cashews that doesn't make sense! please help.

Answer 1

cost of almonds = $3.00 per pound

cost of cashews ---- 1.7(3) or $5.10 per pound

let the amount of cashews she bought be x pounds

so 9(3) + 5.1x = 4(9+x)
27 + 5.1x = 36 + 4x
1.1x = 9
x = appr 8.18 pounds

So the total mixture weighs 17.18 pounds of which 9 pounds were almonds
percentage of almonds = 9/17.18 = appr.524
or 52.4%

Answer 2

To solve this problem, let's break it down step by step:

1. Start by finding the cost per pound of almonds:
Divide the total cost of almonds ($27) by the number of pounds of almonds (9). This gives you the cost per pound of almonds: $27/9 = $3.00 per pound.

2. Next, find the cost per pound of cashews:
It is given that the cost per pound of cashews is 70% more than the cost of almonds. To calculate this, we need to add 70% of the cost of almonds to the original cost:
70% of $3.00 = 0.70 * $3.00 = $2.10
So, the cost per pound of cashews is $3.00 + $2.10 = $5.10.

3. Now, let's figure out the ratio of almonds to cashews in the mixture. Let's assume the weight of cashews is C pounds. Since the total weight of the mixture is 9 pounds, we can write the following equation:
C + 9 = 9 (since the total weight is 9 pounds)

4. To find the cost per pound of the mixture, we can use the weighted average formula:
($3.00 * 9 + $5.10 * C) / (9 + C) = $4.00
Simplifying this equation, we get:
(27 + 5.1C) / (9 + C) = 4

5. Now, solve the equation to find the value of C:
Cross-multiplying and simplifying gives us:
27 + 5.1C = 4(9 + C)
27 + 5.1C = 36 + 4C
Subtracting 4C from both sides gives:
1.1C = 9
Dividing both sides by 1.1 gives us:
C = 8.18 (rounded to two decimal places)

6. Finally, calculate the percentage of almonds in the mixture:
The weight of almonds is 9 pounds, and the total weight of the mixture is 9 + 8.18 = 17.18 pounds.
So, the percentage of almonds in the mixture is (9 / 17.18) * 100 = 52.31% (rounded to two decimal places).

Therefore, the answer is that approximately 52.31% of the mixture by weight is almonds.