Question

A sheet metal shop ordered 60 pounds of tin for $30 and 20 pounds of zinc alloy for a total cost of $480. A second purchase, at the same price, included 40 pounds of tin and 70 pounds of zinc alloy. The total cost was $770. Find the total cost per pound of the tin and of the zinc alloy.

Answer 1

The total cost per pound of tin is approximately $-3.85 and the total cost per pound of zinc alloy is approximately $13.06.

Step-by-step explanation:

To find the total cost per pound of tin we need to set up a system of equations using the given information.

Let's denote the cost per pound of tin as 'x' and the cost per pound of zinc alloy as 'y'.

We have the following equations:

60x + 20y = 30

40x + 70y = 770

To solve this system, we can use the method of substitution or elimination.

Let's use the method of elimination:

Multiply the first equation by 4 and the second equation by 3 to eliminate 'x'.

240x + 80y = 120

120x + 210y = 2310

Subtract the second equation from the first equation:

120x + 40y = 90

120x + 210y = 2310

Subtract the second equation from the first equation:

120x + 40y - 120x - 210y = 90 - 2310

-170y = -2220

y = -2220 / -170 = 13.0588

Substitute the value of 'y' back into one of the original equations:

60x + 20(13.0588) = 30

60x + 261.176 = 30

60x = 30 - 261.176

60x = -231.176

x = -231.176 / 60 = -3.8529

Based on the calculations, the total cost per pound of tin is approximately $-3.85 and the total cost per pound of zinc alloy is approximately $13.06.