Answer:
The cost of a piece of dark meat is <u>$0.70</u> and the cost of a piece of white meat is <u>$0.85</u>.
Step-by-step explanation:
Given:
At Clucker's Chicken, a bucket of 4 pieces of dark meat and 5 pieces of white meat costs 7.05.
A bucket of 3 pieces of dark meat and 8 pieces of white meat costs 8.90.
Now, to find the cost of a piece of dark meat and the cost of a piece of white meat.
Let the cost of a piece of dark meat be ![x.](https://tex.z-dn.net/?f=x.)
And the cost of a piece of white meat be ![y.](https://tex.z-dn.net/?f=y.)
A bucket of 4 pieces of dark meat and 5 pieces of white meat costs $7.05.
So,
![4x+5y=7.05](https://tex.z-dn.net/?f=4x%2B5y%3D7.05)
.......(1)
Now, a bucket of 3 pieces of dark meat and 8 pieces of white meat costs $8.90.
![3x+8y=8.90](https://tex.z-dn.net/?f=3x%2B8y%3D8.90)
Substituting the value of
from equation (1) we get:
![3(\frac{7.05-5y}{4})+8y=8.90](https://tex.z-dn.net/?f=3%28%5Cfrac%7B7.05-5y%7D%7B4%7D%29%2B8y%3D8.90)
![\frac{21.15-15y}{4} +8y=8.90](https://tex.z-dn.net/?f=%5Cfrac%7B21.15-15y%7D%7B4%7D%20%2B8y%3D8.90)
![\frac{21.15-15y+32y}{4} =8.90](https://tex.z-dn.net/?f=%5Cfrac%7B21.15-15y%2B32y%7D%7B4%7D%20%3D8.90)
<em>Multiplying both sides by 4 we get:</em>
![21.15-15y+32y=35.60](https://tex.z-dn.net/?f=21.15-15y%2B32y%3D35.60)
![21.15+17y=35.60](https://tex.z-dn.net/?f=21.15%2B17y%3D35.60)
<em>Subtracting both sides by 21.15 we get:</em>
![17y=14.45](https://tex.z-dn.net/?f=17y%3D14.45)
<em>Dividing both sides by 17 we get:</em>
![y=0.85](https://tex.z-dn.net/?f=y%3D0.85)
<u>The cost of a piece of white meat = $0.85.</u>
Now, substituting the value of
in equation (1) we get:
![x=\frac{7.05-5y}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B7.05-5y%7D%7B4%7D)
![x=\frac{7.05-5\times 0.85}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B7.05-5%5Ctimes%200.85%7D%7B4%7D)
![x=\frac{7.05-4.25}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B7.05-4.25%7D%7B4%7D)
![x=\frac{2.8}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2.8%7D%7B4%7D)
![x=0.70.](https://tex.z-dn.net/?f=x%3D0.70.)
<u>The cost of a piece of dark meat = $0.70.</u>
Therefore, the cost of a piece of dark meat is <u>$0.70</u> and the cost of a piece of white meat is <u>$0.85</u>.