The owner of a home decorating shop wants to mix dried rose petals selling for $6 per pound, dried lavender selling for $4 per pound, and buckwheat hulls selling for $3 per pound to get 10 pounds of a mixture that would sell for $3.70 per pound. She wants to use twice as many pounds of rose petals as lavender. How many pounds of each should she use?
lavender --- x
rose pedals --2x
buckwheat --- 10 - 3x
4x + 6(2x) + 3(10-3x) = 3.7(10)
4x + 12x + 30 - 9x = 37
I will let you finish it
To solve this problem, let's assign variables to represent the unknown quantities.
Let:
x = pounds of dried lavender
2x = pounds of dried rose petals (since the owner wants to use twice as many pounds of rose petals as lavender)
10 - 3x - 6x = pounds of buckwheat hulls (since the total weight is 10 pounds)
Now we can set up the equation based on the cost per pound of the mixture:
($4 * x) + ($6 * 2x) + ($3 * (10 - 3x - 6x)) = ($3.70 * 10)
Simplifying the equation:
4x + 12x + 30 - 9x - 18x = 37
Combine like terms:
-11x + 30 = 37
Now we can isolate the variable by subtracting 30 from both sides:
-11x = 37 - 30
-11x = 7
Finally, divide both sides by -11 to solve for x:
x = 7 / -11
x = -0.64 (approximately)
Since the number of pounds cannot be negative, we disregard this solution.
Therefore, it is not possible to create a mixture with the given conditions.