0

# A coffee merchant combines coffee that costs \$7 per pound with coffee that costs \$3.60 per pound. How many pounds of each should be used to make 26 lb of a blen

A coffee merchant combines coffee that costs \$7 per pound with coffee that costs \$3.60 per pound. How many pounds of each should be used to make 26 lb of a blend costing \$6.15 per pound?

### 3 Answers by Expert Tutors

Steve P. | Patient and Knowledgable Math and Chemistry TutorPatient and Knowledgable Math and Chemis...
4.8 4.8 (5 lesson ratings) (5)
0
First you want to set up two equations. Then substitute one into the other to solve:

Let x be pounds of \$7 coffee and y be pounds of \$3.60 coffee which equals the total pounds of coffee:

x+y=26

The total cost of blended coffee is calculated by adding the total cost of the two different coffees together:

7.00(x)+360(y)=6.15(26)

To solve for one variables use the substitution method:

x+y=26

x=26-y

7(26-y)+3.6y=159.90

182-7y+3.6y=159.90

3.4y=-22.1

y=6.5lb

x=26-6.5=19.5lb

So it takes 19.5lb of the \$7/lb coffee and 6.5lb of the \$3.50/lb coffee to make 26lb of the blended coffee at \$6.15/lb.

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
0
X - amount of \$7 coffee amount
26 - X = amount \$3.60 mixed

\$7X + ( 26- X) \$3.6 = 26(\$ 6. 15 )

7x - 3.6 X + 26 (3.6) = 26( 6.15)

3.4 X =  26( 6.15- 3.6)

3.4 X = 26 ( 2.55)

X = 26( 2.55)
3.4
X = 19.5 lb      lb of \$7 coffee.

26 - 19.5 = 6.5 lb

lb of \$3.60 coffee mixed

The key is to choose a variable for unknown, what is problem asking to find, and convert the
English statements, wording of the problem to algebraic equations and solve.

Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
0
Hi Wesley;
FIRST COFFEE...\$7.00/pound, x pounds
SECOND COFFEE...\$3.60/pound, (26-x)pounds
[(\$7.00/pound)(x pounds)]+[(\$3.60/pound)((26-x)pounds)]=(\$6.15/pound)(26 pounds)
Let's first verify that all units are aligned.
\$/pound is in all facets of the equation.  These cancel...
[(\$7.00/pound)(x pounds)]+[(\$3.60/pound)((26-x)pounds)]=(\$6.15/pound)(26 pounds)
[(7.00)(x pounds)]+[(3.60)((26-x)pounds)]=(6.15)(26 pounds)
The unit of pounds is in the numerator of all facets of the equation.  This cancels...
[(7.00)(x pounds)]+[(3.60)((26-x)pounds)]=(6.15)(26 pounds)
[(7.00)(x)]+[(3.60)(26-x)]=(6.15)(26)
All units align.  We may begin calculations...
[(7.00)(x)]+[(93.60)-(3.60x)]=159.90
Please note that because one of the units is dollars, I am maintaining all figures to two digits to the right of the decimal point.
[(3.40)x]+(93.60)=159.90
Let's subtract 93.60 from both sides...
(-93.60)+[(3.40)x]+(93.60)=159.90-93.60
3.40x=66.30
Let's divide both sides by 3.40
(3.40)x/(3.40)=66.30/3.40

x=19.50 pounds...FIRST COFFEE
26-x=6.50 pounds...SECOND COFFEE