Almonds worth $4.05 per pound were mixed with walnuts worth $4.15 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 the mixture was $100.88? (Hint: Use x to represent the pounds of walnuts.)
Give the value and mixture
Find the pounds for the almonds.
Let x represent the pounds of walnuts.
Then the pounds of almonds would be x + 16.
The total value of the almonds would be 4.05(x + 16) and the total value of the walnuts would be 4.15x.
The total value of the mixture is 100.88, so we can set up the equation:
4.05(x + 16) + 4.15x = 100.88
Expanding the equation and combining like terms:
4.05x + 64.8 + 4.15x = 100.88
8.2x + 64.8 = 100.88
8.2x = 36.08
x = 4.409756097
So the pounds of walnuts used is approximately 4.41 pounds.
To find the pounds of almonds, we can substitute this value back into the expression x + 16:
x + 16 = 4.41 + 16 = 20.41
So the pounds of almonds used is approximately 20.41 pounds.
Therefore, the value of the mixture is $100.88 and the pounds used for the almonds is approximately 20.41 pounds.