The sum of a number and two times a smaller number is 98. the bigger number is 22 less than three times the smaller number. the two numbers are .

The two numbers are 24 and 50

Solution:

Let the bigger number be "b"

Let the smaller number be "s"

Given that sum of a number and two times a smaller number is 98

We can frame a equation as:

bigger number + two times a smaller number = 98

b + 2s = 98 eqn 1

Also given that bigger number is 22 less than three times the smaller number

bigger number = 22 less than three times the smaller number

bigger number = three times the smaller number - 22

b = 3s - 22 eqn 2

Let us solve eqn 1 and eqn 2 to find values of "b" and "s"

Substitute eqn 2 in eqn 1

3s - 22 + 2s = 98

5s - 22 = 98

5s = 98 + 22

5s = 120

Substitute s = 24 in eqn 2

b = 3(24) - 22

b = 72 - 22

Thus the two numbers are 24 and 50

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