how many dimes did Rosalyn collect?

Question

Rosealyn's company, Snack Attack Inc., owns a few vending machines. Last night she collected $82.50 in dimes and quarters. If Rosalyn collected 50 quarters than dimes, how many dimes did she collect?

Answer 1

Mackenzie's question is missing a key word, and Nathan B's query is putting his finger right on the missing element:  Are there 50 more quarters than dimes, or 50 fewer quarters than dimes?  Obviously these two conditions will not give the same answers.

 

But we can deduce what the correct question must have been by looking at the two possible answers:

 

Let D = # of dimes,  Q = # of quarters.

 

Thinking of the problem in pennies:  A dime is 10 pennies, a quarter is 25 pennies, and $82.50 is 8250 pennies.

This leads to the equation:

 

          10 D + 25 Q = 8250

 

If there are 50 fewer quarters than dimes, then Q = D - 50, so

 

          10 D + 25 (D-50) = 8250

                 35 D - 1250  = 8250

                           35 D  = 9500

                                D  = 9500/35 = 271.428571...

 

Since the number of dimes must be a whole number, this is not an acceptable answer.

Therefore the question has to be specifying that there are 50 more quarters than dimes.

Then Q = D + 50, so

 

          10 D + 25 (D+50) = 8250

                35 D + 1250   = 8250

                            35 D  = 7000

                                 D  = 7000/35 = 200

 

So there are 200 dimes.

And since there are 50 more quarters than dimes, there are 250 quarters.

Answer 2

she collected 700 dimes or $70.  because 50 quarters= 12.50 and 82.50-12.50=$70 

 

10 dimes to a dollar, so $70*10=700 dimes