Question

A health food company makes its 'Superfood Blend' from whey protein, which costs $10.25 per pound, and powdered spirulina, which costs $22.45 per pound. The blend ends up costing $16.35 per pound. If the company has 140 pounds of the whey protein on hand, how many pounds of the spirulina does it need to get in order to make the blend?

Answer 1

Given:

Cost of protein = $10.25 per pound

Cost of spirulina = $22.45 per pound

Cost of blend = $16.35 per pound

Weight of blend = 140 pounds

To find:

The quantity of spirulina it will need to make the blend.

Solution:

Let x be the quantity of protein and y be the quantity of spirulina in the blend. Then,

$x+y=140$                      ...(i)

Equation (i) can be written as:

$x=140-y$                      ...(ii)

$10.25x+22.45y=16.35\times 140$

$10.25x+22.45y=2289$                  ...(iii)

Using (ii) and (iii), we get

$10.25(140-y)+22.45y=2289$

$1435-10.25y+22.45y=2289$

$12.2y=2289-1435$

$12.2y=854$

Divide both sides by 12.2.

$y=\dfrac{854}{12.2}$

$y=70$

Therefore, 70 pounds of the spirulina it will need to make the blend.