SOLUTION: in 2 years, edgar will be three fourths as old as his sister, edna. 2 years ago, he was two thirds as old as she. how old are they

Question 906326: in 2 years, edgar will be three fourths as old as his sister, edna. 2 years ago, he was two thirds as old as she. how old are they
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let a = Egar's present age
let b = Edna's
:
Write an equation for each statement, simplify
:
in 2 years, edgar will be three fourths as old as his sister, edna
a + 2 = (b + 2)
multiply both sides by 4
4(a+2) = 3(b+2)
4a + 8 = 3b + 6
4a = 3b + 6 - 8
4a = 3b - 2
divide both sides by 4, we can use decimals here
a = .75b - .5
:
2 years ago, he was two thirds as old as she. how old are they
a - 2 = (b-2)
multiply both sides by 3
3(a-2) = 2(b-2)
3a - 6 = 2b - 4
3a = 2b - 4 + 6
3a = 2b + 2
Replace a with (.75b-.5)
3(.75b - .5) = 2b + 2
2.25b - 1.5 = 2b + 2
2.25b - 2b = 2 + 1.5
.25b = 3.5
multiply both sides by 4
b = 14 yrs is Edna's age
Find a
a = .75(14) - .5
a = 10.5 - .5
a = 10 yrs is Edgar's age
:
:
See if the check out in the statement:
" 2 years ago, he was two thirds as old as she."
10 - 2 = (14 - 2)
8 = *12
8 = 8
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