SOLUTION: Hi Keith has 82 more stamps than Susan. How many stamps must Susan give to Keith so that she has 120 less than him. Thanks

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Question 1175337: Hi
Keith has 82 more stamps than Susan. How many stamps must Susan give to Keith so that she has 120 less than him.
Thanks
Found 2 solutions by math_helper, Theo:
Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website!

The initial state of things is represented by:
K - S = 82

You want to take away x stamps from Susan and give them (add them) to Keith to make that difference 120:
(K+x) - (S-x) = 120

Simplifying:
K-S + 2x = 120

Note that we know K-S is 82:
82 + 2x = 120
2x = 38
x = 19

Ans: Susan must give stamps to Keith to make it so she has 120 less than him. This of course assumes she has at least 19 stamps.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
let k = the number of stamps that keith has.
let s = the number of stamps that susan has.

keith has 82 more stamps than susan.

the formula for that is:

k = s + 82

let x = the number of stamps that susan must give to keith so that keith will have 120 more stamps than susan.

the formula for that is:

k + x = s - x + 120

add x to both sides of this equation to get:

k + 2x = s + 120

solve for 2x to get:

2x = s + 120 - k

since you were given that k = s + 82, then you can replace k with that to get:

2x = s + 120 - (s + 82)

simplify to get:

2x = s + 120 - s - 82

combine like terms to get:

2x = 38

solve for x to get:

x = 19

susan has to give 19 stamps to keith so that keith will have 120 more stamps than susan.

to confirm, do the following:

you start with k = s + 82

you add 19 to k and subtract 19 from s to get:

k + 19 = s - 19 + 120

since k = s + 82, replace k with s + 82 to get:

s + 82 + 19 = s - 19 + 120

combine like terms to get:

s + 101 = s + 101

subtract s from both sides of the equation to get:

101 = 101

since s dropped out of the equation and the equation is true, then you have an infinite number of possible values for s.

for example:

when s = 100, k = 182.

add 19 to k and subtract 19 from s to get:

k = 201 and s = 81.

k is equal to s + 120 after that transaction because 201 minus 81 = 120.

now assume s is any other number, like 4352.

that makes k equal to 4352 + 82 = 4434.

add 19 to 4434 and subtract 19 from 4352 and you get:

keith has 4453 and susan has 4333.

4453 minus 4333 = 120.

the relationship holds regardless of the number of stamps susan had.

the answer to your question is that susan must give keith 19 stamps so that keith will have 120 more stamps than her.