SOLUTION: In 3 years, Alex will be 3 times as old as his sister Precy. A year ago, Alex was 7 times as old as Precy.How old are they now?

Question 93718: In 3 years, Alex will be 3 times as old as his sister Precy. A year ago, Alex was 7 times as old as Precy.How old are they now?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let A be Alex's present age and P be Precy's present age.
.
If A is Alex's present age, then a year ago he was A-1 years old. And a year ago Precy was
P -1 years old.
At that time Alex's age equaled 7 times Precy's age. So in equation form, a year ago:
.

.
We can multiply out the right side to get:
.

.
Then add +1 to both sides to get rid of the -1 on the left side and the equation becomes:
.

.
Finally, subtract 7P from both sides and we get the standard form:
.

.
This is our first equation. Remember it.
.
If A is Alex's current age, then in 3 years his age will be A + 3. And if P is Precy's present
age, then in 3 years she will be P + 3. We are told that at that time Alex's age will be
3 times Precy's age. In equation form this is:
.

.
Multiply our the right side and you have:
.

.
Get rid of the 3 on the left side by subtracting 3 from both sides to get:
.

.
And finally, put this equation in standard form by subtracting 3P from both sides to
get:
.

.
So now we have a set of equations as follows:
.

.
We can eliminate A by subtracting the two equations vertically in columns to get:
.

.
This can be solved for P by dividing both sides by -4 to get that P (Precy's present age)
is +3.
.
That means that a year ago Precy was 2 and at that time Alex was 7 times as old as she. Therefore,
a year ago Alex was 7*2 or 14 years old. But that was a year ago. That means that this
year Alex is a year older so he is currently 15.
.
So we have that presently Alex is 15 and Precy is 3.
.
Three years from now Alex will be 18 and Precy will be 6. So at that time Alex will be
3 times as old as Precy. That checks so it appears that our answer is correct.
.
The answer is Alex is now 15 and Precy is now 3.
.
Hope this helps you to see your way through this problem.
.
RELATED QUESTIONS
In three years, Alex will be 3 times as old as Precy. A year ago, Alex was 7 times as... (answered by ankor@dixie-net.com)

In 3 years, alex will be 3 times as old as his sister precy. a year ago, alex was 7 times (answered by Fombitz)

PLEASE help me for this :( -- In 3 years, Alex will be 3 times as old as his sister... (answered by scott8148)

in 3 years,alex will be 3 times as old as his sister precy,a year ago alex was 7 times as (answered by Theo)

in 3 years angelo will be 3x as old as his sister Precy, a year ago angelo was 7 times as (answered by Theo,josgarithmetic,greenestamps)

In 3 years,alex will be 3 times as old as his sister Precy.A year ago,Alex was 7 times as (answered by alka001)

in 3 years, alex will be 3 times as old as prency. a year ago, alex was 7 times as old as (answered by mananth)

in 3 years,alex will be 3 times as old as his sisters precy.a year ago,alex was 7 times... (answered by AAfter Search)

please help me to solve this equation.In 3 years ,Alex will be 3 times as old as his... (answered by vleith)