Proportional distribution

The addition of the numerators and the denominators of the ratios of a proportion keep the same ratio.

Example:

A. DIRECT PROPORTIONAL DISTRIBUTION

1. Joseph, Peter and Mary invested 5000, 8000 and 10000€ respectively to develop a company. After a year, the company obtains a 2300€ profit. How much money must each partner receive?

  Joseph must receive 500 €, Peter 800 € and Mary 1000 €

2. Two builders earned 450€ for a job. If one of them worked 4 days and the other worked 5 days, how much money must each one receive?

  The first one must receive 200 € and the other 250 €

B. INVERSE PROPORTIONAL DISTRIBUTION

1. The boss of a company wants to distribute a 225€ punctuality bonus among his employees. The first one has 3 delays this month, the second one 4 delays and the third one 6 delays. How much money from the bonus must each get?

   They must get 100, 75 and 50 € respectively

2. This race has a prize of 1100€ for the first, second and third competitors to be distributed in an inverse proportional way according to their position. How much will each one receive?

  They'll receive 600, 300 and 200 euros respectively

Exercises:

1.- Three friends bought a 15€ lottery ticket, the first one paid 6€, the second one paid 4€ and the third one paid 5€. They have won 3000€ for the ticket, how much money must each of them receive?

2.- One father decided to distribute his fortune between his sons in a proportional partition according to their ages. When he died he had 300000€ and his sons were 20 and 30 years old. How much should each one get?

3.-Two waiters received tips for up to 100€ last month and they decided to distribute that money in an inverse proportional way to the times that they were off work. If Paul has been off work twice and Nora three times, how much should each one receive?

Solutions: 1) 1200, 800 and 1000 €; 2) 120000 and 180000 €; 3) Paul 60 € and Nora 40 €