Question #be0a3

1 Answer
Mar 13, 2017

Answer:

larger number #= 31#

Explanation:

Create two equations using two variables:
#S# = smaller number
#L# = larger number

equation 1: #S + L = 49# and rearrange: #S = 49 - L#

To make them equal subtract #8# from #2L#.

equation 2: #2L -8 = 3S#

Substitute equation 1 into equation 2: #2L - 8 = 3(49 - L)#

Distribute the right side: #2L - 8 = 147 - 3L#

Simplify by adding like terms:
#2L +3L -8 = 147 -3L +3L#
#5L -8 = 147#
#5L -8 +8 = 147 + 8#
#5L = 155#
#L = 155/5 = 31#

#S = 49 - 31 = 18#