Question

Gareth has 15 total quarters and dimes with a total value of $2.10. A photo of a stack of quarters and a stack of dimes is shown. The system of equations can be used to solve for the number of each Gareth has. {Q+D=15 25Q+10D=210 Complete in the table to show the quantities and values of the coins Gareth has.

Answer 1

4 Quarters and 11 Dimes

Step-by-step explanation:

In the first equation, we know that
`D=15-Q` If we plug this into the second equation, we get 25q+10(15-Q)=210. If we simplify this equation, we get 25q+150-10q=210, which can be simplified to 15q+150=210. And since 15q=60, q=4. Then, you subtract 4 from 15, to get 11 dimes. So, there are 4 quarters and 11 dimes. Hopefully, this helps!

Answer 2

To solve for the number of quarters and dimes Gareth has, we can set up a system of equations. Using the elimination method, we find that Gareth has 4 quarters and 11 dimes.

Step-by-step explanation:

To solve this problem, we can use a system of equations. Let Q represent the number of quarters, and let D represent the number of dimes. We can set up two equations:

• Q + D = 15 (equation 1)
• 25Q + 10D = 210 (equation 2)

We can solve this system of equations by substitution or elimination method:

Using the elimination method, we can multiply equation 1 by 10 to match the coefficient of D in equation 2:

10(Q + D) = 10(15)

10Q + 10D = 150

Now we can subtract this equation from equation 2:

(25Q + 10D) - (10Q + 10D) = 210 - 150

15Q = 60

Dividing both sides by 15:

Q = 4

Substituting this value of Q back into equation 1 to find D:

4 + D = 15

D = 11

Therefore, Gareth has 4 quarters and 11 dimes.