Question

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

Factors and multiples
ANSWERED
asked 2021-05-28
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

Expert Answers (1)

2021-05-29

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 determmine the second number by evaluating \(y=2+3x\) as \(x=5\):
\(y=2+3x=2+3(5)=2+15=17\)
Thus the two numbers are then 5 and 17.
Result: 5 and 17

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