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:
12 cups of salad are in the resulting mixture.
Step-by-step explanation:
Four cups of a salad blend have 40% spinach,
So the amount of spinach is,
[tex]=4\times \dfrac{40}{100}[/tex]
Let x amount of salad blend is mixed with 55% spinach.
So the amount of spinach is,
[tex]=x\times \dfrac{55}{100}[/tex]
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,
[tex]=(4+x)\times \dfrac{50}{100}[/tex]
As the amount of spinach is same, so
[tex]\Rightarrow (4+x)\times \dfrac{50}{100}=4\times \dfrac{40}{100}+x\times \dfrac{55}{100}[/tex]
[tex]\Rightarrow \dfrac{50(4+x)}{100}=\dfrac{160+55x}{100}[/tex]
[tex]\Rightarrow 50(4+x)=160+55x[/tex]
[tex]\Rightarrow 200+50x=160+55x[/tex]
[tex]\Rightarrow 55x-50x=200-160[/tex]
[tex]\Rightarrow 50x=40[/tex]
[tex]\Rightarrow x=8[/tex]
So, total amounts of mixture will be 4+8=12 cups.
