Question

When A is added to twice B, the result is 21. When B is added to twice A, the result is 18. What are the two numbers?

Answer 1

When A is added to twice B, the result is 21
$a + 2b = 21$
When B is added to twice A, the result is 18
$b + 2a = 18$
From the first equation;
$a = 21 - 2b$
Substitute the value of a in the 2nd equation
$b + 2(21 - 2b) = 18$
Simplify
$b + 42 - 4b = 18$
Collect like terms
$b - 4b = 18 - 42$
$- 3b = - 24$
Divide both sides by - 3
$b = \frac{24}{ - 3}$
$b = 8$
Substitute the value of b in the first equation
$a + 2b = 21 \\ \\ a + 2(8) = 21$
$a + 16 = 21$
Simplify
$a = 21 - 16 \\ \\ a = 5$
Therefore, A is 5 and B is 8. Hope I helped? ☺️