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
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

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