Question

Four cups of a salad blend containing 40% spinach is mixed with an unknown amount of a salad blend containing 55% spinach. The resulting salad contains 50% spinach.

How many cups of salad are in the resulting mixture?

Answer 1

12 cups of salad in total.

Explanation:

First we have to set a letter to represent the number of cups added, this will be X, and we have to represesent the values like this:

Cups of spinach in inital salad blend: 4(.4)

Cups of spinachs in added salad blend: .55(x)

Total amount of cups of spinach: .50(x+4)

So we know that if we add the inital to the added cups we get the total, so that´s our equation:

`4(.4)+.55x= .50(x+4)\\1.6 + .55x= .50x +2\\.05x=.4\\x=8`

By clearing X we get that the number of cups added is 8, if we originally had 4, we now that the resultant salad will hace 12 cups of mixture.

Answer 2

Let the unknown amount of 55% spinach salad be x.
Amount of spinach
40% * 4 + 55% * x = 50% * (4 + x)
0.4 * 4 + 0.55x = 0.5(4 + x)
1.6 + 0.55x = 2 + 0.5x
0.05x = 0.4
x = 0.4/0.05
x = 8
8 cups of 55% spinach salad were added to 4 cups of 40% spinach salad.
The total amount of salad made is 12 cups.