Almonds worth $4.45 per pound were mixed with walnuts worth $5.15 per pound. How many pounds of each were used if there were 16 more pounds of almonds than there were pounds of walnuts and the value of mixture was $153.76
Let x be the number of pounds of walnuts used.
There were x+16 pounds of almonds used.
The value of the almonds used is 4.45(x+16).
The value of the walnuts used is 5.15x.
The total value of the mixture is 4.45(x+16) + 5.15x = $153.76
Combining like terms, we get 4.45x + 71.2 + 5.15x = 153.76
Combining like terms, we get 9.6x + 71.2 = 153.76
Subtracting 71.2 from both sides, we get 9.6x = 82.56
Dividing both sides by 9.6, we get x = 8.6
There were 8.6 pounds of walnuts used.
Therefore, there were 8.6 + 16 = <<8.6+16=24.6>>24.6 pounds of almonds used. Answer: \boxed{8.6, 24.6}.
Let's assume the number of pounds of walnuts used in the mixture is represented by 'x'.
According to the given information, the number of pounds of almonds used in the mixture is 16 more than the number of pounds of walnuts. So, the number of pounds of almonds used can be represented as 'x + 16'.
The total value of the mixture is $153.76. The value of the almonds used in the mixture can be calculated by multiplying the price per pound ($4.45) by the number of pounds used (x + 16). Similarly, the value of the walnuts used can be calculated by multiplying the price per pound ($5.15) by the number of pounds used (x).
Setting up the equation, we can write:
4.45(x + 16) + 5.15x = 153.76
Now let's solve the equation step-by-step:
Step 1: Distribute the 4.45 to both terms inside the parentheses:
4.45x + (4.45 * 16) + 5.15x = 153.76
Step 2: Simplify the equation by multiplying:
4.45x + 71.20 + 5.15x = 153.76
Step 3: Combine like terms:
9.6x + 71.20 = 153.76
Step 4: Move 71.20 to the right side of the equation by subtracting it from both sides:
9.6x = 153.76 - 71.20
Step 5: Simplify the right side of the equation:
9.6x = 82.56
Step 6: Solve for x by dividing both sides of the equation by 9.6:
x = 82.56 / 9.6
Step 7: Calculate the value of x:
x ≈ 8.6
So, approximately 8.6 pounds of walnuts were used in the mixture.
Now, we can find the number of pounds of almonds used:
x + 16 ≈ 8.6 + 16 ≈ 24.6
Approximately 24.6 pounds of almonds were used in the mixture.
Therefore, approximately 8.6 pounds of walnuts and 24.6 pounds of almonds were used in the mixture.