Mixed nuts. Oh Nuts! sells pistachio kernels for $6.50 per pound and almonds for $8.00 per pound. How much of each type should be used to make a 50-lb mixture that sells for $7.40 per pound?
So far I have, this:
6.50x + 8 (50 - x) = 7.50 (50)
6.50x + 400 - 8x = 375
-1.50x + 400 = 375
-1.50x = 25
x = 25/=1.50
x = 20 pounds of pistachios
so
50 - x = 50 - 20 = 30 pounds of almonds.
Can anyone help to let me know if I got his correct or not or please tell me where I went wrong. Math is not one of my strongest subjects and any help would be great....
Your first row should be:
6.5x + 8(50-x) = 7.4(50)
x=20
Your calculation appears to be correct. Here's a step-by-step breakdown:
Let's assume x represents the number of pounds of pistachio kernels and 50 - x represents the number of pounds of almonds.
1. The cost of pistachio kernels is $6.50 per pound, so the cost of x pounds of pistachio kernels is 6.50x dollars.
2. The cost of almonds is $8.00 per pound, so the cost of (50 - x) pounds of almonds is 8.00(50 - x) dollars.
3. The total cost of the mixture is $7.40 per pound multiplied by 50 pounds, which is 7.40 * 50 = 370 dollars.
Now, use the equation you wrote to solve for x:
6.50x + 8(50 - x) = 7.40 * 50
Simplify the equation step by step:
6.50x + 400 - 8x = 370
-1.50x + 400 = 370
-1.50x = 370 - 400
-1.50x = -30
x = -30 / -1.50
x = 20
So, you need 20 pounds of pistachio kernels.
To find the number of pounds of almonds, subtract x from 50:
50 - 20 = 30
Therefore, you need 30 pounds of almonds.
Your final answer of 20 pounds of pistachio kernels and 30 pounds of almonds is correct.
To solve this problem, you need to set up an equation based on the information given. Let's go through the steps and see where you may have made a mistake.
Let x be the number of pounds of pistachio kernels:
The price of pistachio kernels is $6.50 per pound, so the cost of the pistachio kernels is 6.50x dollars.
The remaining weight in the mixture, 50 - x, represents the number of pounds of almonds:
The price of almonds is $8.00 per pound, so the cost of the almonds is 8.00(50 - x) dollars.
The total cost of the mixture is the sum of the costs of the pistachio kernels and almonds:
6.50x + 8.00(50 - x) = 7.40(50)
Now let's solve this equation step by step:
6.50x + 8.00(50 - x) = 7.40(50)
6.50x + 400 - 8.00x = 370
-1.50x + 400 = 370
-1.50x = 370 - 400
-1.50x = -30
Now, divide both sides of the equation by -1.50 to solve for x:
x = -30 / -1.50
x = 20
You got the correct answer! x = 20 pounds of pistachio kernels.
To find the number of pounds of almonds, substitute x back into the equation:
50 - x = 50 - 20
50 - x = 30
So, you also got the correct answer for the number of pounds of almonds, which is 30.
Therefore, your final answer is 20 pounds of pistachio kernels and 30 pounds of almonds to make a 50-pound mixture that sells for $7.40 per pound. Well done!