matthew mixes pretzels that sell for $1.50 a pound with cereal that sells for $3.00 per pound. he wants to make 12 pounds of mixture to sell for $2.00 a pound. how many pounds of each should he use?

Question

matthew mixes pretzels that sell for $1.50 a pound with cereal that sells for $3.00 per pound. he wants to make 12 pounds of mixture to sell for $2.00 a pound. how many pounds of each should he use?

Answer 1

amount of pretzels ---- x lbs

amount of cereal ----- 12-x lbs

1.5x + 3(12-x) = 2(12)

continue

Answer 2

Let's solve the problem step-by-step:

Step 1: Assign variables for the unknowns.
Let x represent the number of pounds of pretzels to be used.
Let y represent the number of pounds of cereal to be used.

Step 2: Formulate the equations based on the given information.
The total weight of the mixture is 12 pounds, so we have the equation:
x + y = 12

The total cost of the mixture is $2.00 per pound, so we have the equation:
(1.50x + 3.00y) / 12 = 2.00

Step 3: Simplify the second equation.
Multiply both sides of the equation by 12 to eliminate the fraction:
1.50x + 3.00y = 24

Step 4: Solve the system of equations.
Using the first equation (x + y = 12), we can solve for x in terms of y:
x = 12 - y

Substituting this expression into the second equation, we get:
1.50(12 - y) + 3.00y = 24

Simplifying, we have:
18 - 1.50y + 3.00y = 24
1.50y = 6
y = 4

Substitute the value of y back into the first equation to find x:
x + 4 = 12
x = 8

Step 5: Check the solution.
Check if the solution satisfies the second equation:
(1.50(8) + 3.00(4)) / 12 = 2
(12 + 12) / 12 = 2
24 / 12 = 2
2 = 2

Step 6: Answer the question.
Matthew should use 8 pounds of pretzels and 4 pounds of cereal.

Answer 3

To find out how many pounds of each ingredient Matthew should use, let's set up a system of equations.

Let x represent the number of pounds of pretzels and y represent the number of pounds of cereal.

1. The total weight of the mixture should be 12 pounds:
x + y = 12

2. The total cost of the mixture should be 12 pounds multiplied by $2.00 per pound:
1.5x + 3y = 2 * 12

Now we have a system of equations. We can solve it using algebraic methods. Let's solve for x in terms of y from the first equation:

x = 12 - y

Substituting this value of x into the second equation:

1.5(12 - y) + 3y = 2 * 12
18 - 1.5y + 3y = 24
1.5y = 6
y = 4

Now we know that Matthew should use 4 pounds of cereal. Substituting this value of y back into the first equation:

x + 4 = 12
x = 12 - 4
x = 8

Therefore, Matthew should use 8 pounds of pretzels and 4 pounds of cereal to make the 12-pound mixture.