# One number is 2 more than 3 times another. Their

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

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Jozlyn

Let x represent the first number and y represent the second number.
The second number is 2 more than 3 times the first number:
$$\displaystyle{y}={2}+{3}{x}$$
The sum of the two numbers is 22:
$$\displaystyle{x}+{y}={22}$$
Let us replace y by $$2+3x$$ in the previous equation (as $$y=2+3x$$ holds):
$$\displaystyle{x}+{\left({2}+{3}{x}\right)}={22}$$
Combine like terms:
$$\displaystyle{2}+{4}{x}={22}$$
Subtract 2 from each side:
$$\displaystyle{4}{x}={20}$$
Divide each side by 4:
$$\displaystyle{x}={5}$$
Thus we obtain that the first number is x=5
Let us then determmine the second number by evaluating $$\displaystyle{y}={2}+{3}{x}$$ as $$\displaystyle{x}={5}$$:
$$\displaystyle{y}={2}+{3}{x}={2}+{3}{\left({5}\right)}={2}+{15}={17}$$
Thus the two numbers are then 5 and 17.
Result: 5 and 17