Question

Kevin and Randy Muise have a jar containing 53 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $10.25. How many of each type of coin do they have?

The jar contains ____ quarters.
The jar contains ____ nickels.

Answer 1

To solve this problem, you can set up a system of equations. The jar contains 38 quarters and 15 nickels.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's define the number of quarters as 'q' and the number of nickels as 'n'.

We know that the total number of coins is 53, so we have the equation:

q + n = 53

We also know that the total value of the coins is $10.25, which can be expressed as:

0.25q + 0.05n = 10.25

We can now solve this system of equations to find the values of 'q' and 'n'.

First, we can multiply the first equation by 0.05 to make the coefficients of 'q' and 'n' match:

0.05q + 0.05n = 2.65

Next, we can subtract this equation from the second equation:

0.25q + 0.05n - (0.05q + 0.05n) = 10.25 - 2.65

0.2q = 7.6

Dividing both sides by 0.2, we get:

q = 38

Substituting this value of 'q' into the first equation, we can solve for 'n':

38 + n = 53

n = 15

Therefore, the jar contains 38 quarters and 15 nickels.

Answer 2

So here is how you'll get the answer.
Let x be the number of quarters in the jar.
Then 53-x is the number of nickels in the jar.
We also know .25x + 0.05 (53-x) = 10.25
So next, we solve for x.
.25x + 2.65 - 0.05x = 10.25
0.2x +2.65 = 10.25
0.2x = 10.25 -2.65
0.2x = 7.40
x =37
Therefore, there are 37 quarters in the jar.
53-37 is 16. So there are 16 nickels in the jar.
Hope this answer helps.