Question 244886
Let n = the weight of a nail
Let b = the weight of the box
Then
40n + b = 175
20n + b = 95<br>
We now have a system of two equations in two variables. There is a large variety of methods to solve this:<ul><li>Graphing</li><li>Substitution</li><li>Elimination/Linear Combination/Addition</li><li>Cramer's Rule</li><li>and a variety of matrix-based methods</li></ul>
This system is solved fairly easily with either the Substitution or Linear Combination methods. I'll use the later:
Subtract the second equation from the first which results in:
20n = 80
Divide by 20
n = 4
Use this value in one of the original equations to find b:
40(4) + b = 175
160 + b = 175
b = 15<br>
This makes the sum: 4 + 15 = 19. Answer: D.