One Number Is 2 More Than 3 Times Another Their Sum Is 22 Find The Numbers

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One number is 2 more than 3 times another. Their sum is 22. Find the numbers.
8, 14
5, 17
2, 20
4, 18
10, 12

Answer: 5, 17

Explanation

Let x represent the first number and y represent the second number.

The second number is 2 more than 3 times the first number:

y = 2 + 3x

The sum of the two numbers is 22:

x + y = 22

Let us replace y by 2 + 3x in the previous equation (as y = 2 + 3x holds):

x + (2 + 3x) = 22

Combine like terms:

2 + 4x = 22

Subtract 2 from each side:

4x = 20

Divide each side by 4:

x = 5

Thus we obtain that the first number is x = 5

Let us then determine the second number by evaluation y = 2 + 3x as x = 5:

y = 2 + 3x = 2 + 3(5) = 2 + 15 = 17

Thus the two numbers are then 5 and 17.

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