Question

you have $5.00 in quarters and dimes. you have a total of 41 coins. how many of the coins are quarters?

Answer 1

To find the number of quarters, set up a system of equations. Solve the system to find the value of q. The number of quarters is 6.

Step-by-step explanation:

To find out how many of the coins are quarters, we can set up a system of equations. Let's assume the number of quarters is q and the number of dimes is d. We know that the total number of coins is 41, so we have the equation q + d = 41. We also know that the value of the quarters is $5.00 and the value of the dimes is $5.00, so we have the equation 0.25q + 0.10d = 5.00. We can solve this system of equations to find the value of q.

To solve the system of equations, we can multiply the first equation by 0.10 to make the coefficients of d in both equations equal:

0.10q + 0.10d = 4.10

0.25q + 0.10d = 5.00

Now, we can subtract the first equation from the second equation:

0.25q - 0.10q = 5.00 - 4.10

0.15q = 0.90

Dividing both sides of the equation by 0.15, we get q = 6. Therefore, there are 6 quarters.

Answer 2

So, from this information you can set up two equations:
0.1x + 0.25y = 5 dollars and
x + y = 41 coins
where x = how many dimes and y = how many quarters

Solve for either x or y in the second equation, so x = 41 - y and then plug this in for x in the first equation to get:
0.1(41 - y) + 0.25y = 5
4.1 - 0.1y + 0.25y = 5
4.1 + 0.15y = 5
0.15y = 0.9
y = 6
We solved for y and now we know there are 6 quarters, so you can plug this into the second equation to solve for x. We fine that we have 35 dimes. You can always your work by plugging what you get for x and y back into the equations.