SOLUTION: Emily’s age is half John’s age. Four years ago Emily was one-quarter of John’s age in 4 years time. Find the age of each now.

Question 1178975: Emily’s age is half John’s age. Four years ago Emily was one-quarter
of John’s age in 4 years time. Find the age of each now.
Found 3 solutions by josgarithmetic, ankor@dixie-net.com, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
E, for Emily's age;
2E for John's age.

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Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
Emily’s age is half John’s age.
e = .5j
Four years ago Emily was one-quarter of John’s age in 4 years time.
e - 4 = (j + 4)
multiply both sides by 4, get rid of the fraction
4(e - 4) = j + 4
4e - 16 = j + 4
4e = j + 4 + 16
4e = j + 20
replace e with .5j, from the 1st statement
4(.5j) = j + 20
2j - j = 20
j = 20 yrs is John's age now
then
.5(20) = 10 yrs is Emily's age
;
;
Check this in the statement
"Four years ago Emily was one-quarter of John’s age in 4 years time."
10 - 4 = (20 + 4)
6 = (24)

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Emily’s age is half John’s age. Four years ago Emily was one-quarter
of John’s age in 4 years time. Find the age of each now.

Let Emily’s age be E
Since Emily is half John’s age, then John's is: 2E
Four years ago, Emily was E - 4
In 4 years' time. John will be 2E + 4
We then get: 2E + 4 = 4(E - 4)
2E + 4 = 4E - 16
2E - 4E = - 16 - 4
- 2E = - 20
Emily, or
Do you think you can now find John's age?
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