Question

A dairy farmer wants to mix a 80 % protein supplement and a standard 70 % protein ration to make 1500 pounds of a high-grade 75 % protein ration. How many pounds of each should he use?

Answer 1

80% of protein supplement mixed with 70% of protein ration to make 1500 pounds of high grade 75% protein ration

so, let the number of pounds from 80% = x

And the number of pounds from 70% = y

Total pounds = 1500 pounds

so, x + y = 1500

The total concentration = 75%

so,

0.8 x + 0.7 y = 0.75 * 1500

So, the system of equations will be:

x + y = 1500 (1)

0.8 x + 0.7 y = 1125 (2)

solve the equations to find x and y

So,

Multiply the first equation by -0.7

-0.7 x - 0.7 y = -0.7 * 1500

-0.7 x - 0.7 y = -1050 (3)

Add the equations (2) and (3)

(0.8 x + 0.7y) + ( -0.7x - 0.7y ) = -1050 + 1125

0.8 x - 0.7 x + 0.7 y - 0.7 y = 75

0.1 x = 75

divide both sides by 0.1

x = 75/0.1 = 750

Substitute with x at the equation (1)

750 + y = 1500

y = 1500 - 750 = 750

so, the number of pounds from 70% = 750 pounds

And the number of poinds from