SOLUTION: Sierra has a total of 61 dimes and quarters in her piggybank. She has 3 more quarters than dimes. The coins have a total value of $10.90. How many dimes and how many quarters does

Algebra ->  Equations -> SOLUTION: Sierra has a total of 61 dimes and quarters in her piggybank. She has 3 more quarters than dimes. The coins have a total value of $10.90. How many dimes and how many quarters does       Log On


   

Question 1102836: Sierra has a total of 61 dimes and quarters in her piggybank. She has 3 more quarters than dimes. The coins have a total value of $10.90. How many dimes and how many quarters does she have? Write an equation for this situation and use it to solve the problem. [Hint: Use the decimal values of the "c" coins to write an equation.]
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

The condition seems to be SUSPICIOUS, since it imposes 3 (three, THREE) conditions on 2 unknowns.

So, let us look what will happen. 


d + q = 61     (1)    (counting coins)
q = d + 3      (2)    ("3 more quarters than dimes")


Substitute (2) into eq(1). You will get

d + (d+3) = 61  ====>  2d + 3 = 61  ====>  2d = 61-3 = 58  ====>  d = 58%2F2 = 29.


Answer.  Working with the first two parts of the condition (with TWO of the THREE), we get this answer:
                
         29 dimes and 29+3 = 32 quarters.


Now, let us check if the LAST condition is satisfied.

Total value = 29*10 + 32*25 = 1090.


Happily, the third condition is satisfied, so the solution and the problem itself are OK.


But still keep in mind that ONE OF THE THREE CONDITIONS is excessive and unnecessary.


The third condition is a potential source for the condition to be WRONG,
but happily it is not the case here.