Question

8. Value Hardware sells 3-in. finishing nails for 0.99/lb and 2-in finishing nails sell for $1.39/1b. Toni needs 5 lb of nails. If his bill totals $6.15, how many pounds of each size did he buy?

Answer 1

This algebraic problem can be solved by setting up a system of equations. For example, let x be the number of pounds of 3-inch nails that Toni buys, and y be the number of pounds of 2-inch nails that Toni buys. We know that x + y = 5 (since Toni believes a total of 5 pounds of pins) and that 0.99x + 1.39y = 6.15 (since that is the total cost of the nails). We can solve for one of the variables using one equation and then substitute that value into the other equation.

Solving for x in the first equation: x + y = 5

x = 5 - y

Substituting this into the second equation: 0.99(5 - y) + 1.39y = 6.15

4.95 - 0.99y + 1.39y = 6.15

4.95 = 0.4y + 6.15

-1.2 = 0.4y

y = -3

Since the number of pounds of nails cannot be harmful, we know that this solution is not possible. We can check by plugging in y = 3 (possible) into the first equation and seeing that x + 3 = 5, so x = 2.

Hence, Toni bought 2 lb of 3-inch nails and 3 lb of 2-inch nails.

Explanation: