Odell has the same number of quarters,dimes , and nickels . In all he has $4 in change. How many of each did he have

Question

It is any type of strategy to solve this problme

 

Answer 1

A quarter is worth 25¢.  A dime is worth 10¢.  A nickel is worth 5¢.  $4 is 400¢.

 

If x is the number of quarters, then 25x is the value, in cents, for all those quarters.  Similarly for dimes and nickels (this is the important unstated piece of information, because:   25x + 10x +5x = 400).

 

Now, using the distributive property on that equation,

      (25+10+5)x = 400

        40x = 400                       [combine terms]

          x = 10                       [divide both sides by 40]

 

Checking (very important):

  Is     25(10) + 10(10) + 5(10) = 400   ?

            250  + 100  +  50  = 400   ?

                 400 = 400   ?yes

Answer 2

 

q = number of quarters 

d = number of dimes

n = number of nickels

$4 = total change

q = d = n

 

($0.25)q + ($0.10)d + ($0.05)n = $4.00

 

q = d = n ⇒

 

($0.25)q + ($0.10)q + ($0.05)q = $4.00

 

(0.25 + 0.10 + 0.05)q = 4.00

 

0.40q = 4.00

 

q = 4.00/0.40 = 10

 

There are 10 of each.