Who Spent what?

Question

John, Paul, George, and Ringo took Singing lessons. Paul spent a week's pay, John spent only half what Paul spent, Ringo spent $60 more than John and George spent 20% more than Ringo. Combined they spent $392. Who spent what?

Answer 1

Most of the time these 'system of equations' word problems have all the equations there already for you - they are just written in English, not in Math. Reading the problem you can make this translation:-

 

P = w (Paul spent a week's pay) (where w is one weeks pay)

J = P / 2 (John spent only half what Paul spent)

R = 60 + J (Ringo spent $60 more than John)

G = (120%)*R (George spent 20% more than Ringo)

P + J + R + G = 392

 

Now you can rewrite all the interms of 'w' and solve!

 

P = w

J = w / 2

R = 60 + w / 2

G = 72 + 0.6 * w

2.6 * w + 132 = 392 ( <- start with this one )