Question 620614
let b = Beth's age
let m = Mom's age
let d = Dad's age
:
Write an equation for each statement. Arrange to get b and d in terms of m:
;
"Beth's mom is 6 times older than Beth."
m = 6b
or
b = {{{1/6}}}m
:
"Beth's dad is 7 years older than Beth's mom."
d = m + 7

:
"The sum of their ages is 72."
b + m + d = 72
Replace b and d
({{{1/6}}}m) + m + (m+7) = 72
({{{1/6}}}m) + 2m = 72 - 7
({{{1/6}}}m) + 2m = 65
multiply equation by 6, results
m + 6(2m) = 6(65)
13m = 390
m = 390/13
m = 30 yrs is Mom's age
then
b = {{{1/6}}}*30
b = 5 yrs is Beth's age
and
d = 30 + 7
d = 37 yrs is Dad's age
:
:
Check this, find the total
5 + 30 + 37 = 72