Question

Lena's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Lena $4.30 per pound, and type B coffee costs $5.50 per pound. This month, Lena made 160 pounds of the blend, for a total cost of $806.80. How many pounds of type B coffee did she use?

Answer 1

Answer:

Assign variables for unknowns.

Let A be the number of pounds of Type A coffee.

Let B be the number of pounds of Type B coffee.

A + B = 150 ( the total weight of the lend of Type A and Type B).

If one pound of Type A costs $4.15 then A pounds costs 4.15A

If one pound of Type B costs $5.60 then B pounds costs 5.6B

4.15A + 5.6B = 712.40  ( total cost of the blend)

At this point you have two equations with A and B as variables.  You can use substitution or elimination method to solve for A.  

A + B = 150

4.15A + 5.6B =  712.40

Substitution method:

A = 150 - B

4.15(150 - B) +  5.6B = 712.40

622.5 - 4.15B + 5.6B = 712.4

622.5 + 1.45B = 712.4

1.45B = 712.4 - 622.5

1.45B = 89.9

B = 89.9/1.45

B = 62

A = 150 - B

A = 150 - 62

A = 88

ANSWER: Elsa used 88 pounds of Type A blend.

Step-by-step explanation:

Assign variables for unknowns.

Let A be the number of pounds of Type A coffee.

Let B be the number of pounds of Type B coffee.

A + B = 150 ( the total weight of the lend of Type A and Type B).

If one pound of Type A costs $4.15 then A pounds costs 4.15A

If one pound of Type B costs $5.60 then B pounds costs 5.6B

4.15A + 5.6B = 712.40  ( total cost of the blend)

At this point you have two equations with A and B as variables.  You can use substitution or elimination method to solve for A.  

A + B = 150

4.15A + 5.6B =  712.40

Substitution method:

A = 150 - B

4.15(150 - B) +  5.6B = 712.40

622.5 - 4.15B + 5.6B = 712.4

622.5 + 1.45B = 712.4

1.45B = 712.4 - 622.5

1.45B = 89.9

B = 89.9/1.45

B = 62

A = 150 - B

A = 150 - 62

A = 88

ANSWER: Elsa used 88 pounds of Type A blend.