Question

A grocery store is packaging a 150-pound quantity of its special rice blend, which costs $4.95 per pound to make. It is made up of wild rice at $6.45 per pound and long grain brown rice at $3.95 per pound. How many pounds of each should be used to make the blend?

Answer 1

Let x be the number of pounds of wild rice at $6.45 per pound.

Let y be the number of pounds of long grain brown rice at $3.95 per pound.

The total amount of rice is 150 pounds:

x+y=150

Total cost = (price per pound of wild rice * number of pounds of wild rice) + (price per pound of brown rice * number of pounds of brown rice)

Total cost = (6.45 * x) + (3.95 * y)

the total cost is known to be $4.95 per pound for 150 pounds,

(6.45 * x) + (3.95 * y) = 4.95 * 150

6.45x + 3.95y = 742.5

system with 2 equations

x+y=150

6.45x+3.95y=4.95*150=742.5

by substitution: x=150-y

we replace x in the 2nd equation

6.45(150-y)+3.95y=742.5

967.5-6.45y+3.95y=742.5

-2.50y=742.5-967.5

-2.50y= -225

y= 90

we calculate x

x+y= 150

x+90=150

x=150-90=60

to get the special 150-pound rice mix, the grocery store must use 60 pounds of wild rice and 90 pounds of long-grain brown rice.