SOLUTION: please help me with these problems: 1. Olan is 3 years older than his sister, Rose. One-half of Olan's age is 13 yrs. more than 1/4 his sister's age one year ago. Find their age

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Question 393128: please help me with these problems:
1. Olan is 3 years older than his sister, Rose. One-half of Olan's age is 13 yrs. more than 1/4 his sister's age one year ago. Find their ages now.
2. Grace is 4 times as old as Vicky. Five years ago, Vicky was 30 years younger than Grace. Find their present ages.
Thanks. I will appreciate your help in my daughter's homework.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Here is a method you can use on most of these age problems
:
Let L = Olan's present age
Let R = Roses present age
:
Write an equation for each statement:
" Olan is 3 years older than his sister, Rose."
L = R + 3
:
"One-half of Olan's age is 13 yrs. more than 1/4 his sister's age one year ago."
L = 13 + (R-1)
Get rid of those fractions multiply both sides by 4, results:
2L = 4(13) + R - 1
2L = 52 + R - 1
2L = R + 51
Substitute (R+3) for L (1st statement)
2(R+3) = R + 51
2R + 6 = R + 51
2R - R = 51 - 6
R = 45 yrs is Roses age
then
L = 45 + 3
L = 48 yrs is Olan's age
:
Check our solutions in the statement:
"One-half of Olan's age is 13 yrs. more than 1/4 his sister's age one year ago."
(48) = 13 + (45-1)
24 = 13 + 11
:
:
2. "Grace is 4 times as old as Vicky."
G = 4V
:
"Five years ago, Vicky was 30 years younger than Grace."
V - 5 = (G - 5) - 30
V - 5 = G - 35
V = G - 35 + 5
V = G - 30
Replace G with 4V
V = 4V - 30
+30 = 4V - V
30 = 3V
V = 10 is Vicky's present age
then
G = 4(10)
G = 40 is Grace's age
:
:
Check this in the statement:
"Five years ago, Vicky was 30 years younger than Grace."
10 - 5 = 40 - 5 - 30
5 = 40 - 35