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Dominic went into a movie theater and bought 2 drinks and 5 candies, costing a total of $29.25. Colton went into the same movie theater and bought 8 drinks and 7 candies, costing a total of $61.75. Determine the price of each drink and the price of each candy.

 Feb 3, 2020
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Dominic went into a movie theater and bought 2 drinks and 5 candies, costing a total of $29.25. Colton went into the same movie theater and bought 8 drinks and 7 candies, costing a total of $61.75. Determine the price of each drink and the price of each candy.    

 

How much help do you need.  This is a common substitution problem.  I'll get it set up for you.   

 

Let the price of a drink be represented by D    

Let the price of a cancy be represented by C    

 

These two equations are given in the problem              2D + 5C = 29.25    

                                                                                      8D + 7C = 61.75    

 

                                                                                      Can you take it from there?  If not, continue.

 

Let's see now, it looks like the easiest thing to     

do now is multiply both sides of the first one by 4.

That way we can subtract one equation from the   

other, thereby isolating the "C" unknown.                     4 • (2D + 5C) = 4 • 29.25    

 

Multiply it on out                                                            8D + 20C = 117.00    

From this let's subtract the second equation                 8D + 7C = 61.75    

 

and the answer from the above subtraction is                      13C = 55.25    

 

Divide both sides by 13 and obtain                                           C = 4.25    one candy costs $4.25    

 

Plug that value of C back into one of     

the original equations                                                     2D + (5 • 4.25) = 29.25

                                                                                       2D +   21.25     = 29.25

                                                                                                          2D = 29.25 – 21.25    

                                                                                                          2D = 8.00    

                                                                                                            D = 4.00    one drink costs $4.00      

.

 Feb 3, 2020

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