Pip and Sara win some money and share it in the ratio 7:3. Pip gets £36 more than Sara. How much did they get altogether?

Question

Ratio 

Answer 1

 

THe N be the total amount of the winnings and S be the amount Sara has.

Then Pip has (S+36)

 

N = (S+36)+S = 2s + 36

 

Their winnings are in the ration 7 to 3.

So  

 

 7/10 N = S+36 ---> N=  10(S+36)/7

 

 3/10 N = S --->  N = 10S/3

 

They are equal:

 

 10(S+36)/7 = 10S/3

 

cross multiplies

 

30(S+36) = 70S

 

30S + 1080 = 70S

 

1080 = 70S - 30S

 

1080 = 40S

 

 S = 1080/40 = 540/20 = 270/10 = 27

 

Sara has $27.

Pip has $27+36 = 63

 

Together they won 27+63 = 90.

 

Pip has 63/90 = 7/10 = 70% <--- divides by 9 to reduce

Sara has 27/90 = 3/10 = 30% <--- divides by 9 to reduce