SOLUTION: Two numbers have a sum of 50. If the second number is 2 more than 3 times the first number, what are the 2 numbers?

Question 473104: Two numbers have a sum of 50. If the second number is 2 more than 3 times the first number, what are the 2 numbers?

Answer by karaoz(32) (Show Source): You can put this solution on YOUR website!

The unknown values are two numbers.
Let's name them m and n.

Next, translate the relevant information into algebraic statements using m and n.
From the first sentence we know that m + n = 50.
From the second sentence we know that n = 3m + 2 and we know that they want us to to find the values for m and n.

Writing only algebraic statements now, we have:
m + n = 50
n = 3m + 2,
which is the system of 2 equations with 2 unknowns.

We can use the second equation to substitute for n in the first equation.
This way we will get new equation that has only one variable in it.
m + (3m + 2) = 50
Simplifying the above, we have:
4m + 2 = 50.
Taking away 2 from both sides of the equation, we get:
4m + 2 - 2 = 50 - 2
Simplifying,
4m = 48
Dividing both sides of the equation by 4:
m = 12.
We now know the first number m.

We can find the second number from any of the two original equations while using the obtained value for m.
Using the second equation will be easier:
n = 3m + 2
n = 3(12) + 2
n = 36 + 2
n = 38.

The numbers are 12 and 38.

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