# Algebra age problem

James is five years old now and Emma is four years older.

Form a relevant equation and use it to find out how many years it will take until James' and Emma's age in years, multiplied together will make 725 years.

I'm needing help to form the equation. Anyway, from what I've done so far, I know that James will be 25 and Emma will be 29 when their age multiplied together will make 725.

Anyway what I've tried so far:

X(X+4) = 725
25(25+4) = 725

I think the proper equation would be something like this:
X² + 4 = 725
But then wouldn't the next part be something like:
X² = 725 - 4
If so, I have no idea how I'm suppose to get 25 from:
(X = blank)( X = blank) = 721

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danago
Gold Member
James is five years old now and Emma is four years older.

Form a relevant equation and use it to find out how many years it will take until James' and Emma's age in years, multiplied together will make 725 years.

I'm needing help to form the equation. Anyway, from what I've done so far, I know that James will be 25 and Emma will be 29 when their age multiplied together will make 725.

Anyway what I've tried so far:

X(X+4) = 725
25(25+4) = 725

I think the proper equation would be something like this:
X² + 4 = 725
But then wouldn't the next part be something like:
X² = 725 - 4
If so, I have no idea how I'm suppose to get 25 from:
(X = blank)( X = blank) = 721
First part looks ok, but look at the part where youve expanded it. It should be 'X² + 4X = 725'. From there, you can factorize the quadratic into an equation of the form $$(x+a)(x+b)=0$$, and then by looking at the equation, you should easily be able to see value(s) of X that fit. Just use the value that fits the restrictions (since the question is referring to a persons age, obviously the restriction x>0 will apply.)

arildno
Homework Helper
Gold Member
Dearly Missed
First, get used to represent the quantity you are ASKED to find (i.e, "the unkown") EXPLICITLY!

Strategy:
James is 5 years old, Emma 5+4=9 years old.
The number of years FROM NOW till their age product is 725 is what you are asked to find. Denote that quantity by X.

Thus, after X years from now, James' age is 5+X, whereas Emma's age then is 9+X.

Thus, you get the equation:

(5+X)(9+X)=725 (which has the solution X=20)