Answer:
The drawer contains 40 nickels, 20 dimes and 14 quarters.
Step-by-step explanation:
Let d, q and n represent number of dimes, quarters and nickels respectively.
We have been given that there are twice as many nickels as dimes.
![n=2d...(1)](https://tex.z-dn.net/?f=n%3D2d...%281%29)
Further, the number of dimes and quarters sum to 34.
![d+q=34...(2)](https://tex.z-dn.net/?f=d%2Bq%3D34...%282%29)
As the change drawer contains $7.50 made up entirely of quarters, nickels, and dimes.
From equation (2), we will get:
![q=34-d](https://tex.z-dn.net/?f=q%3D34-d)
Substituting equation (1) and equation (2) in equation (3), we will get:
Therefore, drawer contains 20 dimes.
Substitute
in equation (1):
![n=2d](https://tex.z-dn.net/?f=n%3D2d)
![n=2(20)](https://tex.z-dn.net/?f=n%3D2%2820%29)
![n=40](https://tex.z-dn.net/?f=n%3D40)
Therefore, drawer contains 40 nickels.
Substitute
in equation (2):
![20+q=34](https://tex.z-dn.net/?f=20%2Bq%3D34)
![20-20+q=34-20](https://tex.z-dn.net/?f=20-20%2Bq%3D34-20)
![q=14](https://tex.z-dn.net/?f=q%3D14)
Therefore, drawer contains 14 quarters.