please answer

Question

Sarah blends coffee She needs to prepare 150 pounds of blended coffee beans selling for $5.38 per pound. She plans to do this by blending together a high-quality bean costing $6.25 per pound and a cheaper bean at $3.00 per pound. To the nearest pound, find how much high-quality coffee bean and how much cheaper coffee bean she should blend.

Answer 1

There are two methods to solve this problem, substitution and elimination.

From the data you can derive two equations:

 

ax + by = (5.38)(150)                   from the data she needs 150 lbs of coffee that she will sell for 5.38 per pound

(6.25)x + (3.00)y = (5.38)(150)    so (150)(5.38) represents the total cost. This cost is made from x lbs of coffee @    

x + y = 150                                 6.25 per pound and y lbs of coffee @ 3.00 per pound. The total weight is equal to                                                     the weight of the two coffees.

Substitution method:

 

x + y = 150                                           solve for y

x = 150 - y

a(150 - y) + by = (5.38)(150)

6.25(150 - y) + 3.00y = (5.38)(150)

937.5 - 6.25y +3y = 807

-3.25y = -130.5

y = 40.15

 

x + y = 150                                           solve for x

x + 40 = 150

x = 110

 

ax + by = (5.38)(150)

(6.25)(110) + (3.00)(40) = (5.38)(150)        verify in original equation

687.5 + 120 = 807

807.5 = 807                                               does not come out exactly even due to rounding

 

Elimination method:

 

ax + by = (5.38)(150)

6.25x + 3.00y = 807

x + y = 150                                               modify one equation so that when added to the other, one variable

-6.25(x + y) = (150) -6.25                          will be eliminated.

 

6.25x + 3.00y = 807                                   

-6.25(x + y) = -937.5                                      multiply each side of 2nd equation to eliminate x variable

(6.25x + 3y) + (-6.25x - 6.25y) = 807 - 937.5   then solve for y

6.25 x - 6.25x + 3y - 6.25y = -130.5

-3.25y = -130.5

y = 40.15 or 40

 

x + y = 150                                                 solve for x

x + 40 = 150

x = 110