Question

The sum of two numbers is 12. When three times the first number is added to 5 times the second number, the resultant number is 44. How do you find the two numbers?

Answer 1

The first number is `8` and the second number is `4`

Explanation:

We will turn the word problem into an equation to make it easier to solve. I am going to abbreviate "first number" to `F` and "second number to `S`.

`stackrel(F + S)overbrace"the sum of the two numbers" stackrel(=)overbrace"is"stackrel(12)overbrace"12"`

AND:

`stackrel(3F)overbrace"three times the first number" " " stackrel(+) overbrace"is added to" " "stackrel(5S)overbrace"five times the second number" " " stackrel(= 44)overbrace"the resultant number is 44"`

Our two equations from the two bits of information are:
`F + S = 12`
`3F + 5S = 44`

Now let's change the first equation so that we can solve for one of the variables.
`F + S = 12`
`F = 12 - S`

Now substitute it into the second equation and solve:
`3F + 5S = 44`
`3(12 - S) + 5S = 44`
`36 - 3S + 5S = 44`
`36 + 2S = 44`
`2S = 8`
`S = 4`

Now that we know `S`. substitute it into one of the equations and solve it for F. Either equation would work, but I will use this one:
`F = 12 - S`
`F = 12 - 4`
`F = 8`

CHECK:
`3F + 5S = 44` this should be right if our numbers are correct.

`3(8) + 5(4) = 44`
`24 + 20 = 44`
`44 = 44` True, so our numbers are correct.