Question

The difference of two numbers, a and b, is 21. The difference of 5 times a and two times b is 18. What are the values of a and b?

Answer 1

Welcome to OC. You have asked an algebra question. The question has already labeled the two numbers:
One number is called "a", the other is called b..

the next thing given is "the difference of two numbers, a and b is 21. Using algebra we then can write a - b = 21. We are further given expressed in algebra: 5a - 2b =18.
The key to this is a and b have the same value in both expressions. You have two equations and 2 unknowns. It is a system: a - b = 21 and 5a - 2b = 18.

Use the substitution method to solve. in first equation express a in terms of b like:
a = b + 21, now substitute for a in the 2nd equation:
5(b + 21) - 2b = 18 solve for b
5b + 105 -2b = 18
3b = 18 - 105
3b = -87
b=-29 Now substitute the value of (-29) of b in the first equation.
a- (-29) = 21
a + 29 = 21
a= -8

As always you want to verify: -8 - (-29) = 21, getting -8 + 29 = 21
21=21 First one checks out
Now do 2nd one
5(-8) - (2*-29) = 18
-40 - (-58) = 18
-40 +58 = 18
18=18 Also checks.