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?

## 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

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# 3 Answers

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.

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.

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