some oranges are shared among 5 people. each person gets 3 more than he or she would have gotten if the oranges were shared among 8 people. how many oranges are there

Question

anonymous · Answer

40 oranges

anonymous · Answer

40 oranges / 5 people = 8 oranges per person
40 oranges / 8 people = 5 oranges per person

mathmale · Answer

Good. 

But I'd suggest that learning to use an algebraic approach would be of more help in the long run, and also that we helpers should be making an effort to involve Alein8mo in the solution of this problem.

Let x be the total number of oranges.  Let y be the number of oranges that each of 8 people receive.  Then x/8 =y.  Having this information allows us to eliminate either variable x or variable y.

Our task is to determine the number of oranges we started with, so we eliminate y and keep x.

To do that, we'll need another relationship / equation.

"Some oranges are shared among 5 people.  Each person gets 3 more than he or she would have gotten if the oranges were shared among 8 people."  Note that we've defined y to be " he or she would have gotten if the oranges were shared among 8 people."

Thus, x/5 = y+3.

We must now solve the set of simultaneous equations

                               x/8 = y                and                    x/5 = y+3.

Try solving these simultaneous equations for x.

Hint:  Substitute y = x/8 into the second equation.  This eliminates y and leaves us with an equation in x only.

@Alein8mo ?