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?

1 Answer
Mar 22, 2018

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.