Question

Nick's weight to rick's weight is in the ratio 7:5. if nick loses 4 kg and rick puts on 10 kg, their weights will be the same. how heavy is nick?

Answer 1

Nick is 49 kg

Explanation:

Let N be Nick's weight in kg and R be Rick's weight in kg

We have the ratio

`(N)/(R)=(7)/(5)` ==>
`R=(5N)/(7)`

The second statement can be mathematically stated as

N - 4 = R + 10 (If Nick loses 4kg and Rick gains 10kg they are both same wt)

Substitute for R in terms of N

`N - 4 = (5N)/(7)+10N`

`N - (5N)/(7) = 14`

Multiplying both sides by 7 will get rid of the denominator

7N -5N = 98 ==> 2N=98 ==> N=49

We can easily verify our answer

If Nick is 49, Rick must be (5/7)49 = 35.

N-4 = 49-4 = 45

R+10 = 35 + 10 = 45

And we see they are both the same value