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

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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

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