Answer:
Nick is 49 kg
Step-by-step explanation:
Let N be Nick's weight in kg and R be Rick's weight in kg
We have the ratio
[tex]\frac{N}{R}=\frac{7}{5}[/tex] ==> [tex]R=\frac{5N}{7}[/tex]
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
[tex]N - 4 = \frac{5N}{7}+10N[/tex]
[tex]N - \frac{5N}{7} = 14[/tex]
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
