SOLUTION: Please help me turn this into an equation, I am having a lot of trouble understanding it. Apples are collected in a basket for six people. One third, one fourth, one eighth, and

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Please help me turn this into an equation, I am having a lot of trouble understanding it. Apples are collected in a basket for six people. One third, one fourth, one eighth, and      Log On


   

Question 558261: Please help me turn this into an equation, I am having a lot of trouble understanding it.
Apples are collected in a basket for six people. One third, one fourth, one eighth, and one fifth of the apples are given to four people, respectively. The fifth person gets ten apples, and one apple remains for the sixth person. Find the original number of apples in the basket.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Let N be the number of apples

%28matrix%285%2C1%2C+all%2C+of%2Cthe%2CN%2C+apples%29%29-%28matrix%289%2C1%2C+1%2F3%2Cof%2Cthe%2C+N%2C+apples%2Cfor%2C+the%2C+first%2C+person%29%29-%28matrix%289%2C1%2C+1%2F4%2Cof%2Cthe%2C+N%2C+apples%2Cfor%2C+the%2C+second%2C+person%29%29-%28matrix%289%2C1%2C+1%2F8%2Cof%2Cthe%2C+N%2C+apples%2Cfor%2C+the%2C+third%2C+person%29%29-%28matrix%289%2C1%2C+1%2F5%2Cof%2Cthe%2C+N%2C+apples%2Cfor%2C+the%2C+fourth%2C+person%29%29-%28matrix%286%2C1%2C+ten%2C+apples%2Cfor%2C+the%2C+fifth%2C+person%29%29 = %28matrix%286%2C1%2C+one%2C+apple%2Cfor%2C+the%2C+sixth%2C+person%29%29


                    N - 1%2F3N - 1%2F4N - 1%2F8N - 1%2F5N - 10 = 1 

Add 10 to both sides

                         N - 1%2F3N - 1%2F4N - 1%2F8N - 1%2F5N = 11 

Multiply every term by 120:

    120·N - 120·1%2F3N - 120·1%2F4N - 120·1%2F8N - 120·1%2F5N = 120·11 

                  120N - 40N - 30N - 15N - 24N =  1320 

                                           11N = 1320
                                          
                                             N = 1320%2F11
                                              
                                             N = 120

Answer = 120 apples.

Edwin