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.