A store is having a sale on walnuts and chocolate chips. For 5 pounds of walnuts and 3 pounds of chocolate chips the total cost is $23. For 2 pounds of walnuts and 12 pounds of chocolate chips, the total cost is $47. Find the cost for each pound of walnuts and each pound of chocolate chips.

Answer 1

Let x be the cost per pound of walnuts and y be the cost per pound of chocolate chips.

From the given information, we can create a system of two equations:
5x + 3y = 23
2x + 12y = 47

To solve this system of equations, we will first multiply the first equation by 2 to eliminate x:
10x + 6y = 46
2x + 12y = 47

Next, we will subtract the second equation from the first equation:
8x - 6y = -1

Now we can solve for x:
8x - 6y = -1
8x = 6y - 1
x = (6y - 1) / 8

Now we can substitute this value of x into one of the original equations to solve for y. Let's use the first equation:
5x + 3y = 23
5((6y - 1) / 8) + 3y = 23
(30y - 5) / 8 + 3y = 23
30y - 5 + 24y = 184
54y = 189
y = 189 / 54
y = 21 / 6
y = $3.50

Now that we have found the cost per pound of chocolate chips, we can substitute this value back into the equation for x to solve for the cost per pound of walnuts:
2x + 12y = 47
2x + 12(3.50) = 47
2x + 42 = 47
2x = 5
x = $2.50

Therefore, the cost per pound of walnuts is $2.50 and the cost per pound of chocolate chips is $3.50.