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