Question

The sum of three numbers is 106. The second number is 2 times the third. The first number is 6 more than the third. What are the numbers?First numberSecond number Third number

Answer 1

Let's call the numbers a, b and c.

The first statement tells us that the sum of the three numbers is 106, so:

`a+b+c=106.`

The second statement tells us that the second number is two times the third so:

`b=2c\text{.}`

The final statement tells us that the first number is 6 more than the third, so:

`a=c+6.`

This gives us a system of three equations with three variables. Let's take the value of a given by the third equation, use it in the first one and isolate another variable:

`(c+6)+b+c=106,`
`2c+b+6=106,`
`2c+b=100,`
`b=100-2c\text{.}`

Let's take this value of b and use it in the second equation:

`100-2c=2c,`
`100=4c,`
`c=25.`

Now we know the exact value of c, so let's go back to the third equation:

`a=25+6=31,`

and now we also know the exact value of a, so let's go back to the second equation:

`b=2(25)=50.`

So, the first number (a) is 31, the second (b) is 50 and the third (c) is 25.

31+50+25=106.