Question

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 space plus space y space equals space 72.50 x space plus space 1.90 y space equals space 15.82 what is the difference between the number of pounds of strawberries and the number of pounds of grapes in the mix

Answer 1

53 pounds

Explanation:

Given:-

- The number of pounds of strawberries = x

- The number of pounds of grapes = y

- The system of equation relating "x"and "y" is:

x + y = 72.5

x +1.9y = 15.82

Find:-

what is the difference between the number of pounds of strawberries and the number of pounds of grapes in the mix

Solution:-

- We will use the first equation and determine "x" in terms of "y":

x = 72.5 - y ..... Eq3

- Substitute Equation 3 in Equation 2 and solve for y:

72.5 - y + 1.9y = 15.82

y = (15.82 - 72.5) / 0.9

y = 63

- Now substitute the value of "y" into Eq3:

x = 72.5 - 63

x = 9.5 ≈ 10

- The difference in pounds of strawberries and grapes in a mix would be:

y - x = 63 - 10 = 53 pounds

Answer 2

The difference between the number of pounds of strawberries and the number of pounds of grapes in the mix is 33.42 pounds.

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)`

Subtracting equation 2 from equation 1, we get:

`2.9y = 56.68\\y=(56.68)/(2.9) \\y=19.54pounds`

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`

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`

The difference between the number of pounds of strawberries and the number of pounds of grapes in the mix is 33.42 pounds.