There are 24 coins made up of quarters and dimes which amount to $3.90.How many of each kind of coin are there?

Question

 word problems

Answer 1

Let Q & D be the number of quarters and dimes, respectively. Then we can write two equations, for the total number of coins, and for the total value in cents:

 

Q + D = 24

25Q + 10D = 390

 

Dividing the second equation by 5, we get

 

5Q + 2D = 78.

 

Multiplying the first equation by 2, we have

 

2Q + 2D = 48.

 

Subtracting these, we find

 

3Q = 30

 

or Q=10, which, when subsituting in the last equation, we can use to find D:

 

2(10) + 2D = 48

20 + 2D = 48

10 + D = 24      (dividing by 2, or  2D=28  subtracting 20)

D = 14.

 

So there are 10 quarters and 14 dimes.

 

This is a uniquely determined solution since we had two (non-equivalent) equations in two unknowns (that was solvable).