Final answer:
The cost per pound of almonds is $9, and the cost per pound of pistachios is $14. Using algebra, we set up an equation with the given total price and differential cost between nuts to find the price per pound for each type of nut.
Step-by-step explanation:
Let's solve the problem of figuring out the cost per pound of pistachios and almonds that Venetta buys. We're told that pistachios cost $5 more per pound than almonds and that Venetta buys 2 pounds of pistachios and 4 pounds of almonds, paying a total of $64. We'll use this information to set up an equation to solve for the price per pound of almonds, which we'll call 'x', and then use that to find the price per pound of pistachios, which will be 'x + $5'.
Solution:
First, we determine the total cost of the almonds, which is 4x. The cost of pistachios is 2(x + 5), adding the $5 more per pound. So, the equation to represent the total cost is:
4x + 2(x + 5) = $64
Simplifying, we get:
4x + 2x + 10 = 64
6x + 10 = 64
Subtract 10 from both sides:
6x = 54
Now, divide by 6
x = 9
So, the cost per pound of almonds is $9. Then, the cost per pound of pistachios is $9 + $5 = $14.
This matches the given information that Venetta spent $64 in total for nuts, as $9 times 4 pounds is $36 for almonds, and $14 times 2 pounds is $28 for pistachios, which adds up to $64.