System of equations

Question

The sum of three numbers is 12. The third number is two minus that the sum of the second number and three times the first number.

Five times the first number equals the sum of the second and third number. Calculate the numbers.

Answer 1

This problem is solved using a system of three equations. I'll get you started. The first step is to translate the given information into equations.

Let the three numbers in order be a, b, and c.

"The sum of three numbers is 12" may be translated to a + b + c = 12 (Call that equation #1.)

The second statement is a little confusing, but take it a little at a time: "The third number is two minus that the sum of the second number and three times the first number."

The third number (c) is (=) two minus (2-) the sum of the second number (b) and (+) three times the first number (3a). So... c = 2 -(b + 3a) That's equation #2.

Five times the first number (5a) equals (=) the sum of the second and third number (b+c) So...

5a = b + c

So you have...

(1) a + b + c = 12

(2) c = 2 -(b + 3a)

(3) 5a = b + c

I'll let you take it from here, but start by arranging all three equations in standard from, similar to Equation #1. Then use substitution and/or elimination to get rid of two of the variables.