SOLUTION: A box containing 40 nails weighs 175 grams. The same box with 20 nails weighs 95 grams. What is the sum of the weight of the box and one nail? (A) 4 (B) 9.5 (C) 15 (D) 19 (E) 69

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Question 244886: A box containing 40 nails weighs 175 grams. The same box with 20 nails weighs 95 grams. What is the sum of the weight of the box and one nail?
(A) 4 (B) 9.5 (C) 15 (D) 19 (E) 69.7
Found 2 solutions by Theo, jsmallt9:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
we have the weight of the box which is represented by b.

we have the weight of the nails which is represented by n.

first formula is:

b + 40*n = 175

second formula is:

b + 20*n = 95

in both equations, solve for b.

b + 40*n = 175 becomes b = 175 - 40*n

b + 20*n = 95 becomes b = 95 - 20*n

since they both equal to b, then they are equal to each other so we get:

175 - 40*n = 95 - 20*n

add 40*n to both sides of this equation and subtract 95 from both sides of this equation to get:

175 - 95 = -20*n + 40*n

combine like terms to get:

80 = 20*n

divide both sides of this equation by 20 to get:

n = 4 grams

substitute in your first equation of b + 40*n = 175 to get:

b + 40*4 = 175

subtract 40*4 from both sides of equation and simplify to get:

b = 175 - 160

simplify further to get:

b = 15

use the value of b = 15 and n = 4 in the second equation to get:

b + 20*n = 95 becomes:

15 + 20*4 = 95 becomes:

15 + 80 = 95 which is true so the values for b and n are good.

You have:

b = 15
n = 4

b + n = 19

Answer to your question is:

the box and one nail weigh 19 grams which is selection D.


Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = the weight of a nail
Let b = the weight of the box
Then
40n + b = 175
20n + b = 95

We now have a system of two equations in two variables. There is a large variety of methods to solve this:
  • Graphing
  • Substitution
  • Elimination/Linear Combination/Addition
  • Cramer's Rule
  • and a variety of matrix-based methods

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

This makes the sum: 4 + 15 = 19. Answer: D.