The larger of two numbers is 1 less than 8 times the smaller. Their sum is 179. How do you find the numbers?

1 Answer
Oct 2, 2015

Answer:

The two numbers are #20# and #159#

Explanation:

Define
#color(white)("XXX")b = #bigger (larger) number
#color(white)("XXX")s = #smaller number

We are told
[1]#color(white)("XXX")b = 8s-1#
[2]#color(white)("XXX")b+s=179#

Substituting #(8s-1)# for #b# (from [1]) into [2]
[3]#color(white)("XXX")8s-1+s = 179#

Simplify
[4]#color(white)("XXX")9s=180#

[5]#color(white)("XXX")s=20#

Substituting #20# for #s# in [2]
[6]#color(white)("XXX")b+20=179#

[7]#color(white)("XXX")b=159#