Question:
The sum of two numbers is fifteen. Three times the smaller is equal to two times the larger. Find the numbers
Answer:
The numbers are 6 and 9
Solution:
Let the smaller number be "a" and the larger number be "b"
Given that sum of two numbers is 15
smaller number + larger number = 15
a + b = 15 ----- eqn 1
Three times the smaller is equal to two times the larger
3(smaller number) = 2(larger number)
3a = 2b ---- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "a" and "b"
From eqn 1,
a = 15 - b ------- eqn 3
Substituting eqn 3 in eqn 2,
3(15 - b) = 2b
45 - 3b = 2b
5b = 45
b = 9
Therefore from eqn 3,
a = 15 - b = 15 - 9 = 6
a = 6
Summarizing the results:
Smaller number "a" = 6
Larger number "b" = 9