A merchant wants to mix gummy worms worth $7 per pound and gummy bears worth $3 per pound to make 30 pounds of a mixture worth $4.60 per pound. How many pounds of each type of candy should he use?
How would I write out this problem to solve?
If x lbs of worms, then
7x + 3(30-x) = 4.60*30
This is just like the interest problem, which is also a mixture problem.
To determine how many pounds of each type of candy the merchant should use, we can set up a system of equations based on the given information.
Let's define:
- x as the number of pounds of gummy worms.
- y as the number of pounds of gummy bears.
Based on the information given, we have the following equations:
Equation 1: The total weight of the mixture is 30 pounds:
x + y = 30
Equation 2: The cost of the mixture per pound is $4.60:
(7x + 3y) / 30 = 4.60
To solve the system of equations, we can follow these steps:
Step 1: Rearrange Equation 2 to isolate one variable:
7x + 3y = 4.60 * 30
7x + 3y = 138
Step 2: Multiply Equation 1 by 3 to eliminate y:
3x + 3y = 90
Step 3: Subtract Equation 2 from Equation 3:
(3x + 3y) - (7x + 3y) = 90 - 138
-4x = -48
Step 4: Solve for x by dividing both sides by -4:
x = (-48) / (-4)
x = 12
Step 5: Substitute the value of x back into Equation 1 to solve for y:
12 + y = 30
y = 30 - 12
y = 18
Therefore, the merchant should use 12 pounds of gummy worms and 18 pounds of gummy bears to make a 30-pound mixture worth $4.60 per pound.
Huh? It's already written out. That's how I got the equation. Can you not solve the equation?
If you find x, that's how many lbs of worms you need. The rest (30-x) is bears.