Please help solve word Problem

Question

Geraldo has dowel pieces measuring 10 inches and 11 inches long. He places a number of the pieces end-to-end. They form a line 76 inches long. How many pieces of each size dowel does he have?

Answer 1

 

Let x = number of 10 inch pieces

Let y = number of 11 inches pieces

 

    10x + 11y = 76

 

X and Y must be integers.  By trial and error,

 

   If x = 1, ... 10(1) + 11y = 76

                    10 + 11y = 76

                    11y = 66

                       y = 6

 

                There could be 1 piece that is 10-inches and

                                      6 pieces that are 11-inches 

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    If x = 2, ... 10(2) + 11y = 76
                     20 + 11y = 76
                     11y = 56
                        y = 5.09 ... discard .. not an integer

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Similarly, x cannot equal to 3, 4, 5, 6, 7 ... (none of those produces

integer values for y) ... and x cant be larger than 7,

because 8 times 10 is 80 ... too long

 

So there is 1 10-inch piece and 6 11-inch pieces.