Paul and Ian have $280 altogether. 1/6 of Paul's money is $12 less than 1/5 of lan's money.

Question

(a) How much money does each boy have?
(b) Find the ratio of Paul's money to Ian's money.

Answer 1

Let P be Paul's money and I be Ian's money.
We know that P + I = 280.
We also know that 1/6P = 1/5I - 12.
Multiplying both sides of the equation by 30, we get 5P = 6I - 360.
Multiplying both sides of the equation by 6, we get 30P = 36I - 2160.
Subtracting the first equation from the second equation, we get 29P = 35I - 1880.
Dividing both sides of the equation by 29, we get P = (35I - 1880)/29.
Substituting the value of P into the first equation, we get (35I - 1880)/29 + I = 280.
Multiplying both sides of the equation by 29, we get 35I - 1880 + 29I * 29*280.
Combining like terms, we get 64I = 1880 + 8120.
Adding the two numbers, we get 64I = 10000.
Dividing both sides of the equation by 64, we get I = 156.25.
Substituting the value of I into the equation P = (35I - 1880)/29, we get P = (35(156.25) - 1880)/29 = 133.75.
Therefore, Paul has $133.75 and Ian has $156.25.
The ratio of Paul's money to Ian's money is 133.75/156.25 = 0.855/1.