Question

One number is 2 less than a second number. Twice the second number is 9 less than 3 times the first. Find the two numbers.

Answer 1

Answer:

27

Step-by-step explanation:

Let the two numbers, smaller be x and larger be y.

As per statement, one number is 3 less than a second number.

x = y - 3…Eq..1

Twice the second number is 3 less than 3 times the first.

3x = 2y + 3…Eq..2

Now putting the value of x from Eq..1 to Eq…2

3x = 2y + 3

3 (y - 3) = 2y + 3

3y - 9 = 2y + 3

3y - 2y = 3 + 9

y = 12

The larger number is 12.

Now putting the value of y in Eq. 1 to get the value of x

x = y - 3

x = 12 - 3

x = 9

The smaller number is 9

Answer the two numbers, smaller is 9 and larger is 12.

To check the correctness of answer, substituting the derived values of two numbers in the Eq…2

3x = 2y + 3

3 × 9 = 2 × 12 + 3

27 = 24 + 3

27 =27