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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.
