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

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.

Let x the amount 55% salad blend

Y = the amount of 50%

The equation:

4 + x = y

4(0.40) +0.55x = 0.50y

Solving the equation

X = 8 cups

Y = 12 cups of the resulting mixture

Answer 2

12 cups of salad are in the resulting mixture.

Explanation:

Four cups of a salad blend have 40% spinach,

So the amount of spinach is,

`=4* (40)/(100)`

Let x amount of salad blend is mixed with 55% spinach.

So the amount of spinach is,

`=x* (55)/(100)`

As both the cups were mixed, so the net amount will be (4+x) cups.

The result has 50% spinach, so the amount of spinach is,

`=(4+x)* (50)/(100)`

As the amount of spinach is same, so

`\Rightarrow (4+x)* (50)/(100)=4* (40)/(100)+x* (55)/(100)`

`\Rightarrow (50(4+x))/(100)=(160+55x)/(100)`

`\Rightarrow 50(4+x)=160+55x`

`\Rightarrow 200+50x=160+55x`

`\Rightarrow 55x-50x=200-160`

`\Rightarrow 50x=40`

`\Rightarrow x=8`

So, total amounts of mixture will be 4+8=12 cups.