Answer:
1668.75
Step-by-step explanation:
Answer:
and ![y=8](https://tex.z-dn.net/?f=y%3D8)
Step-by-step explanation:
Given:
Equation 1:
![500y-600x=2800](https://tex.z-dn.net/?f=500y-600x%3D2800)
Simplifying the above equation by dividing both sides by 100
![\frac{500y-600x}{100}=\frac{2800}{100}](https://tex.z-dn.net/?f=%5Cfrac%7B500y-600x%7D%7B100%7D%3D%5Cfrac%7B2800%7D%7B100%7D)
![\frac{500y}{100}-\frac{600x}{100}=28\\\\5y-6x=28](https://tex.z-dn.net/?f=%5Cfrac%7B500y%7D%7B100%7D-%5Cfrac%7B600x%7D%7B100%7D%3D28%5C%5C%5C%5C5y-6x%3D28)
Equation 2:
![400y-400x=2400](https://tex.z-dn.net/?f=400y-400x%3D2400)
Simplifying the above equation by dividing both sides by 400.
![\frac{400y-400x}{400}=\frac{2400}{400}](https://tex.z-dn.net/?f=%5Cfrac%7B400y-400x%7D%7B400%7D%3D%5Cfrac%7B2400%7D%7B400%7D)
![\frac{400y}{400}-\frac{400x}{400}=6\\\\y-x=6](https://tex.z-dn.net/?f=%5Cfrac%7B400y%7D%7B400%7D-%5Cfrac%7B400x%7D%7B400%7D%3D6%5C%5C%5C%5Cy-x%3D6)
Now the system of equation is:
(1a) ![5y-6x=28](https://tex.z-dn.net/?f=5y-6x%3D28)
(2a) ![y-x=6](https://tex.z-dn.net/?f=y-x%3D6)
Solving by elimination
Multiplying equation (2a) with ![-5](https://tex.z-dn.net/?f=-5)
![-5(y-x)=-5\times 6](https://tex.z-dn.net/?f=-5%28y-x%29%3D-5%5Ctimes%206)
(2b) ![-5y+5x=-30](https://tex.z-dn.net/?f=-5y%2B5x%3D-30)
Adding equations (1a) and (2b) in order to eliminate ![y](https://tex.z-dn.net/?f=y)
![5y-6x=28](https://tex.z-dn.net/?f=5y-6x%3D28)
+ ![-5y+5x=-30](https://tex.z-dn.net/?f=-5y%2B5x%3D-30)
We get ![-x=-2](https://tex.z-dn.net/?f=-x%3D-2)
∴ ![x=2](https://tex.z-dn.net/?f=x%3D2)
Plugging
in equation (2a).
![y-2=6](https://tex.z-dn.net/?f=y-2%3D6)
Adding
both sides.
![y-2+2=6+2](https://tex.z-dn.net/?f=y-2%2B2%3D6%2B2)
∴ ![y=8](https://tex.z-dn.net/?f=y%3D8)
Answer:
60
Step-by-step explanation:
After adding 88 red marbles, there are 50 blue marbles out of the 204 marbles total.
Let the number of blue marbles to be added be x.
![\frac{50+x}{204+x}=\frac{5}{12} \\ \\ 600+12x=1020+5x \\ \\ 420=7x \\ \\ x=60](https://tex.z-dn.net/?f=%5Cfrac%7B50%2Bx%7D%7B204%2Bx%7D%3D%5Cfrac%7B5%7D%7B12%7D%20%5C%5C%20%5C%5C%20600%2B12x%3D1020%2B5x%20%5C%5C%20%5C%5C%20420%3D7x%20%5C%5C%20%5C%5C%20x%3D60)
Move everything to the left hand side and factor, follow this