00:01
The ratio of the ages of mr.
00:03
Vahendra and rahul is 7 to 2.
00:06
After 8 years, their ages will be in the ratio of 8 to 3.
00:11
Find their present ages.
00:14
Now, since we have a word problem, i usually try to draw a picture or draw a table to help me organize information.
00:21
I've decided since we are working with a lot of numbers here, just looking at their ages, i think a table would be more appropriate.
00:30
Okay, so i have the two people.
00:34
I have a row for each of them.
00:36
And for the columns, i have their ages.
00:40
Now, if we take a look at the first sentence, we have the ratio of their ages present day, which is seven to two.
00:50
Now, i can't just write seven and two here because they are not necessarily seven and two currently.
00:57
That's just a ratio in which your ages are in.
01:00
So one way to kind of go about doing this is maybe sticking in a dummy variable.
01:06
So i can say seven times this variable, maybe i'll call it x, seven times this x, and then i'll have two times the same x.
01:18
So in that way it keeps that ratio seven to two.
01:22
Okay, after eight years, we have another ratio, eight to three.
01:27
Now i can potentially use another dummy variable.
01:32
I can maybe do 8 y and 3y.
01:36
One thing that i'm little hesitant about is using too many variables because then it makes things a lot more difficult for us to solve.
01:43
So i think i'm not going to do that.
01:45
What i'm going to do instead is i'm going to add 8 to each of the present years, present ages, so 7x plus 8.
01:57
Because that's what they're going to be in eight years.
02:00
So 2x plus 8.
02:03
And in these two numbers or these two expressions, i'll put it in the ratio of 8 to 3.
02:10
So what does that look like? that actually creates the equation that we're looking for.
02:15
So we have the 7x plus 8 over 2x plus 8.
02:21
This will be in the ratio of 8 to 3.
02:24
So i'm making it equal to the fraction 8 over.
02:28
3.
02:29
And then we can solve this.
02:31
So we'll solve it for x and then we'll throw our x into our table...