SOLUTION: Seattle Star blends whole bean coffee worth $0.93 per pound with half bean coffee worth $1.20 per pound to get 30 pounds of a coffee blend worth $1.02 per pound. How many pounds o
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Question 5762: Seattle Star blends whole bean coffee worth $0.93 per pound with half bean coffee worth $1.20 per pound to get 30 pounds of a coffee blend worth $1.02 per pound. How many pounds of each type of coffee does she use?
Found 2 solutions by guapa, CharStar:
Answer by guapa(62) (Show Source): You can put this solution on YOUR website!
Let x represent the amount of the $1,20 coffee. Then 30-x represents the amount of the $0,93 coffee
Use the following guideline:
Amount of coffee worth $1,20 + Amount of coffee worth $0,93 = Total worth $1,02
1,20(x) + 0,93(30-x) = 1,02(30)
Now let'ss simplify the terms:
1,2x + 27,9 - 0,93x = 30,6 Combine like terms
0,27x +27,9 = 30,6 Substract 27,9 from both sides
0,27x +27,9 - 27,9 = 30,6- 27,9
0,27x = 2,7 Divide both sides by 0,27
0,27x/0,27 = 2,7/0,27
x = 10
Therefor: 30-x = 30-10 = 20
Check:
1,2(10)+0,93(30-10)= 1,02(30)
12 +18,6 = 30,6
30,6 = 30,6
So, 10 pounds of half bean coffee worth $1,20 per pound are mixed with 20 pounds of whole bean coffee worth $0,93 per pound.
You can use this guideline not only for mixture problems of this type(amount + price) but also for problems with amount and percent.
Hope this helps
Answer by CharStar(110) (Show Source): You can put this solution on YOUR website!
Whole Bean Coffee - $0.93
Amount in lbs = x
Total of Each - 0.93x
Half Bean Coffee - $1.20
Amount in lbs = 30-x
Total Cost of each = $1.20(30-x)
Mixture =$1.02
Amount in lbs = 30
Total Cost of each = $1.02(30)
$0.93x + 1.20(30-x) = $102.(30)
$0.93x + 36.00 - 1.20x = 30.60
-36.00 from both sides and Add the x
$0.27 x = 5.40
x=20
Check your answer
$0.93(20)=$18.60
$1.20(30-20) = $12.00
$18.60 + $12.00 = $36.00
1.02(30) = $36.00
Hope that helps you.
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