# 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.
a) 8, 14
b) 5, 17
c) 2, 20
d) 4, 18
e) 10, 12

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Beverly Smith
Let x be the first number and y be the second one.
If the sencond number is 2 more that 3 times the first number, we have:
$$\displaystyle{y}={2}+{3}{x}$$
The sum of them is 22, so
$$\displaystyle{x}+{y}={22}$$
Replace y by $$\displaystyle{2}+{3}{x}$$ in the previous equation
$$\displaystyle{x}+{\left({2}+{3}{x}\right)}={22}$$
$$\displaystyle{x}+{2}+{3}{x}={22}$$
$$\displaystyle{4}{x}+{2}={22}$$
$$\displaystyle{4}{x}={22}-{2}$$
$$\displaystyle{4}{x}={20}$$
$$\displaystyle{x}={5}$$ is the first number, then the second is:
$$\displaystyle{y}={2}+{3}\times{5}$$
$$\displaystyle{y}={17}$$
Thus, the answer is 5 and 17.
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recoronarrv
The answer is B (5, 17)