Question 974170
let a = Alicia's age
let b = brother's age
let m = Mom's age
:
Write an equation for each statement;
:
Alicia's brother is one third as old as alicia.
b = {{{1/3}}}a
:
 Alicia's mother is five years more than twice Alicia's age.
m = 2a + 5
:
If the sum of their age is 45,
a + b + m = 45
Replace b with {{{1/3}}}a. replace m with (2a+5)
a + {{{1/3}}}a + (2a+5) = 45
multiply equation by 3, get rid of the fraction
3a + a + 3(2a+5) = 3(45)
3a + a + 6a + 15 = 135
10a = 135 - 15
10a = 120
a = 120/10
a = 12 yrs is Alicia's age
:
:
Check this by finding the ages of b and m
b = {{{1/3}}}(12)
b = 4
and
m = 2(12) + 5
m = 29
Find the sum with these values
12 + 4 + 29 = 45