sam has $21.40 in dimes and quarters, for a total of 100 coins. How many of each kind of coin does he have?

Question

i need to find out how to solve

Answer 1

Let x be the number of dimes and y be the number of quarters.

 

He has a hundred coins total, so x + y = 100 (Equation 1)

 

If he has x dimes, each dime is 10¢ =  $0.10, in total he has $ 0.10x in dimes.

 

If he has y quarters, each quarter is 25¢ = $0.25, in total he has $ 0.25y in quarters.

 

Adding the above two quantities,  he has 0.1x + 0.25y in dimes and quarters, and we know the total amount of money he has is $21.40, so 0.10x + 0.25y = 21.40 (Equation 2).

 

In summary, our two equations are

 

x + y = 100 (Equation 1)

0.10x + 0.25y = 21.40 (Equation 2)

 

We have to solve these two simultaneously for x and y.  An easy way to do this is to multiply equation 2 by 10 on the left and right hand sides, which gives

 

x + 2.5y = 214 (Equation 3).

 

Now, subtract equation (1) from equation (3) to eliminate x.

 

1.5y = 114

 

Solve this for y, and that will give you the number of quarters.  Then, substitute your answer for y into equation (1), and solve for x, which will give you the number of dimes.