SOLUTION: Campbell has 2 more toys than he needs in order to have one-half the number of toys Noah has. Campbell is 3 short of three-quarters the number of toys Noah has. How many toys does

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Campbell has 2 more toys than he needs in order to have one-half the number of toys Noah has. Campbell is 3 short of three-quarters the number of toys Noah has. How many toys does       Log On


   

Question 1033401: Campbell has 2 more toys than he needs in order to have one-half the number of toys Noah has. Campbell is 3 short of three-quarters the number of toys Noah has. How many toys does Campbell have?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let c represent the number of toys that campbell has.
let n represent the number of toys that noah has.

c = .5 * n + 2
this means that campbell has 2 more toys than half the toys that noah has.

c = .75 * n - 3
this means that campbell has 3 less toys than three quarters of the toys that noah has.

you have two equations that need to be solved simultaneously.

they are:

c = .5 * n + 2
c = .75 * n - 3

subtract the first equation from the second equation to get 0 = .25 * n - 5

add 5 to both sides of the equation to get 5 = .25 * n

divide both sides of the equation by .25 to get 5/.25 = n

solve for n to get n = 20

noah has 20 toys.

campbell has 2 more than half of noah's toys means that campbell has 12.

campbell has 3 less than three quarters of noah's toys means that campbell has 12.

the numbers check out.

noah has 20.
campbell has 12.