A vendor has 40 quarts of lemonade to sell. He has 12 containers. Some of the containers hold 4 quarts and some hold 2 quarts. How many of each does he have?

Question

A vendor has 40 quarts of lemonade to sell. He has 12 containers. Some of the containers hold 4 quarts and some hold 2 quarts. How many of each does he have?

Answer 1

Not being a math teacher, I resorted to trial-and-error -- and found that the vendor needs twice as many 4-quart containers as 2-quart containers.

Answer 2

there will be 8 four quart containers and 4 two quart containers that will eqeal 12 containers and uses all 40 quarts

Answer 3

Let's assume he has x containers that hold 4 quarts, and y containers that hold 2 quarts.

According to the information given, the total number of containers he has is 12. So we have the equation: x + y = 12. (Equation 1)

Also, the total amount of lemonade he has is 40 quarts, which equals the sum of quarts in each container. Therefore, we have: 4x + 2y = 40. (Equation 2)

To solve the system of equations using the substitution method, let's solve equation 1 for x:
x = 12 - y.

Now, substitute this value in equation 2:
4(12 - y) + 2y = 40.
48 - 4y + 2y = 40.
48 - 2y = 40.
-2y = 40 - 48.
-2y = -8.
Divide both sides by -2:
y = (-8) / (-2).
y = 4.

Now, substitute the value of y in equation 1:
x + 4 = 12.
x = 12 - 4.
x = 8.

Therefore, the vendor has 8 containers that hold 4 quarts and 4 containers that hold 2 quarts.

Answer 4

To find out how many containers hold 4 quarts and how many hold 2 quarts, we can use a system of equations.

Let's assume the number of containers that hold 4 quarts is "x" and the number of containers that hold 2 quarts is "y".

To create an equation, we know that the total number of containers is 12, so we have the equation:

x + y = 12

We also know that the total number of quarts of lemonade is 40. The containers that hold 4 quarts each will contribute 4x quarts, and the containers that hold 2 quarts each will contribute 2y quarts. So we have another equation:

4x + 2y = 40

Now, we can solve this system of equations to find the values of x and y.

First, let's rearrange the first equation:

x = 12 - y

Substitute this value of x into the second equation:

4(12 - y) + 2y = 40

Now simplify this equation:

48 - 4y + 2y = 40

Combine like terms:

-2y = 40 - 48

-2y = -8

Divide both sides by -2:

y = -8 / -2

y = 4

Now substitute this value of y back into the first equation to solve for x:

x + 4 = 12

x = 12 - 4

x = 8

Therefore, the vendor has 8 containers that hold 4 quarts and 4 containers that hold 2 quarts.