Answer:
The difference between the number of pounds of strawberries and the number of pounds of grapes in the mix is 33.42 pounds.
Step-by-step explanation:
I think that the right question is:
In the system of equations shown, x represents the number of pounds of strawberries, and y represents the number of pounds of grapes in a fruit mix. x y = 15.82 and x - 1.90y = 72.5. what is the difference between the number of pounds of strawberries and the number of pounds of grapes in the mix
Given that:
x represents the number of pounds of strawberries, and y represents the number of pounds of grapes in a fruit mix.
The equation relating x and y is given by the equation:
![x+y=72.5...(1)\\x-1.9y=15.82...(2)](https://tex.z-dn.net/?f=x%2By%3D72.5...%281%29%5C%5Cx-1.9y%3D15.82...%282%29)
Subtracting equation 2 from equation 1, we get:
![2.9y = 56.68\\y=\frac{56.68}{2.9} \\y=19.54pounds](https://tex.z-dn.net/?f=2.9y%20%3D%2056.68%5C%5Cy%3D%5Cfrac%7B56.68%7D%7B2.9%7D%20%5C%5Cy%3D19.54pounds)
Putting y = 19.54 in equation 1 to get:
![x+y=72.50\\x+19.54=72.50\\x=72.50-19.54=52.96\\x=52.96pounds](https://tex.z-dn.net/?f=x%2By%3D72.50%5C%5Cx%2B19.54%3D72.50%5C%5Cx%3D72.50-19.54%3D52.96%5C%5Cx%3D52.96pounds)
Therefore, the difference between the number of pounds of strawberries and the number of pounds of grapes in the mix is given by:
![x-y=52.96-19.54=33.42pounds](https://tex.z-dn.net/?f=x-y%3D52.96-19.54%3D33.42pounds)
The difference between the number of pounds of strawberries and the number of pounds of grapes in the mix is 33.42 pounds.