Linear Equation Word Problem (below)

Question

The sum of Eric’s and Bob’s weights is 9 times the difference of their weights. The positive difference of their weights is also 240 pounds less than the sum. If Eric weighs less than Bob, find Bob’s weight.

(how do I solve this?)

Answer 1

The first step to solving a word problem is to write out what we know in equation form. I will be using Bob's weight is B and Eric's weight is E. In this case, we have 2 unknowns, so we need 2 equations to solve for both values.

From "If Eric weighs less than Bob":

(1) E < B which means B - E > 0 (This will be used for the positive difference)

From "The sum of Eric's and Bob's weights is 9 times the difference of their weights":

(2) B + E = 9 * (B - E)

From "The positive difference of their weights is also 240 pounds less than the sum":

(3) B - E = (B + E) - 240

From (3), we can solve for Eric's weight by cancelling B and rearranging the equation.

(4) -E = E - 240

(5) 240 = 2 * E

(6) E = 120

Now that we have E, we can plug this into (2) to solve for B.

(7) B + 120 = 9 * (B - 120)

(8) B + 120 = 9 * B - 1080

(9) 1200 = 8 * B

(10) B = 1200/8 = 150

Now we have found Bob's weight.