Megan has dimes and nickles in her purse. There are 28 coins with a value of $2.25 .hiw many of each type of coin does she have?

Question

Megan has only nickels and dimes (28) that add up to $2.25 haw many of each type of coin are there

Answer 1

Let the number of dimes be d and number of nickles be n. You know that a dime is 10 cents or .10 of a dollar, a nickle is 5 cents or .05 of a dollar. 

 

Set up: 

The total number of coins is given to be 28 

d+n=28

 

The total value of these 28 coins is $2.25

.10d+.05n=2.25

 

Solve:

With the first equation solve for n by subtracting d from both sides of the equation

n=28-d

 

Plug n=28-d into .10d+.05n=2.25

.10d+.05(28-d)=2.25

.10d+1.4-.05d=2.25

 

Combine like-terms by adding .10d with .05d

.05d+1.4=2.25

 

Subtracting both sides by 1.4

.05d = 2.25-1.4=0.85

 

Solve for d by dividing both sides by .05

d = 17

 

Find the number of nickles by plugging d=17 back into n=28-d

n=28-17=11

 

Answer: Number of dimes is 17 and nickles is 11

 

Check: Total number of coins (17+11) is 28

.10(17)+.05(11)=2.25