To begin with the amount of lemonade in a jug was 5 times the amount in a cup. Another 150 ml was then poured into each if the containers. The amount of lemonade in the jug was then 3 times the amount in the cup. How much lemonade was in the jug to begin with?
cup = x
jug = 5x
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5x+150 = 3(x+150)
x = 150
So the jug started with 5x = 750 ml
check:
after adding 150 ml, the jug had 900 and the cup had 300.
Well, this is one juicy problem. Let me squeeze out the solution for you.
Let's assume the amount of lemonade in the cup is 'x' ml. If the amount of lemonade in the jug is 5 times that, then it would be 5x ml.
After pouring an additional 150 ml into each container, we now have 'x + 150' ml in the cup and '5x + 150' ml in the jug.
According to the next statement, the amount of lemonade in the jug is 3 times the amount in the cup. So we can set up the equation:
5x + 150 = 3(x + 150)
Now, it's time to simplify this equation and solve for 'x'.
5x + 150 = 3x + 450
2x = 300
x = 150
Therefore, the amount of lemonade in the jug to begin with was 5x, which translates to 5 * 150 = 750 ml.
Voila! The jug was filled with 750 ml of lemonade right from the start. Sip sip, hooray!
Let's assume the amount of lemonade in the cup to start with is x ml.
According to the given information, the amount of lemonade in the jug is 5 times the amount in the cup. Therefore, the amount of lemonade in the jug is 5x ml.
After pouring 150 ml into each container, the amount of lemonade in the cup becomes x + 150 ml, and in the jug, it becomes 5x + 150 ml.
According to the next statement, the amount of lemonade in the jug is 3 times the amount in the cup. So, we can set up the following equation:
5x + 150 = 3(x + 150)
Simplifying the equation, we get:
5x + 150 = 3x + 450
Combine like terms:
5x - 3x = 450 - 150
2x = 300
Divide both sides by 2:
x = 150
Therefore, the initial amount of lemonade in the jug was 5 times the amount in the cup, which is 5 * 150 ml = 750 ml.
To solve this problem, let's break it down step by step.
Let's start by assigning variables to the unknowns in the problem. Let's call the initial amount of lemonade in the jug "J" and the initial amount of lemonade in the cup "C."
From the problem, we know that the amount of lemonade in the jug was 5 times the amount in the cup. So we can write the equation: J = 5C.
Next, we are told that another 150 ml was poured into each container. After pouring, the amount of lemonade in the jug was 3 times the amount in the cup. This gives us the second equation: J + 150 = 3(C + 150).
Now we have two equations:
J = 5C (equation 1)
J + 150 = 3(C + 150) (equation 2)
To solve this system of equations, we can use substitution or elimination. Let's use substitution to solve it.
Since equation 1 already gives us J = 5C, we can substitute this expression for J in equation 2:
5C + 150 = 3(C + 150)
Now, we can simplify and solve for C:
5C + 150 = 3C + 450
2C = 300
C = 150
So, the initial amount of lemonade in the cup was 150 ml.
To find the initial amount of lemonade in the jug, we can substitute this value back into equation 1:
J = 5C
J = 5(150)
J = 750
Therefore, the initial amount of lemonade in the jug was 750 ml.