two years ago pete was three times as old as his cousin claire. 2 years before that, pete was four times as old as claire. in how

two years ago pete was three times as old as his cousin claire. 2 years before that, pete was four times as old as claire. in how many years will the ratio of their ages be 2 : 1?

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1. After 4 years ratio of their ages be 2 : 1
How do you calculate the ratio?
The steps of calculating a ratio are as follows:
Establish the ratio’s function. Choosing what you want your ratio to show should be your first step. Every ratio will use a different set of data, so you need to make sure you are using the right data to provide you with the information you need.
Organize your formula. Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.
Make the equation work. To calculate your ratio, divide data A by data B.
Let the present age of pete be P and claire be C.
According to question:
Two years ago pete was three times as old as his cousin claire.
⇒ P – 2 = 3(C – 2)
⇒ P – 2 = 3C – 6
⇒ P = 3C – 6 + 2
⇒ P = 3C – 4 ………………(1)
Also,  2 years before that, pete was four times as old as claire.
⇒ P – 4 = 4(C – 4)
⇒ P – 4 = 4C – 16
⇒ P = 4C – 16 + 4
⇒ P = 4C – 12 ………………(2)
Equating eq(1) and eq(2)
4C – 12 = 3C – 4
4C – 3C = -4 + 12
C = 8
Substitute the value of C in eq(1) we get,
P = 3(C) – 4 = 3(8) – 4 = 24 – 4 = 20
Let x be the number of years until Pete is twice as old as his cousin.
20 + x = 2(8 + x)
20 + x = 16 + 2x
20 – 16 = 2x – x
4 = x
Therefore, after 4 years ratio of their ages be 2 : 1