The sum of two numbers is fifteen. three times the smaller is equal to two times the larger.

The sum of two numbers is fifteen. Three times the smaller is equal to two times the larger. Find the numbers

The numbers are 6 and 9

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

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