Question

$149,000 estate is to be divided between two charities so that one charity receives $18,000 less than the other. How much will each charity receive?

Answer 1

For this case, the first thing we must do is define variables.
 We have then:
 x: amount of money for charity 1.
 y: amount of money for charity 2.
 We now write the system of equations that models the problem:
 $x + y = 149000 y = x-18000$
 We solve the system.
 Using substitution we have:
 $x + (x-18000) = 149000$
 Clearing x:
 $2x = 149000 + 18000 x = 167000/2 x = 83500$
 Then, the value of the second charity is:
 $y = x-18000 y = 83500-18000 y = 65500$
 Answer:
 charity 1 = $ 83500
 charity 2 = 65500 $