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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