To begin with the amount of lemonade in a jug was 5 times the amount in a cup. Another 15th 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?
I don't know how much 1/15 is. 1/15 of what?
Let's go step by step to find the amount of lemonade in the jug to begin with.
Step 1: Let's assume the amount of lemonade in the cup to be x.
Since the amount of lemonade in the jug was 5 times the amount in the cup, the amount of lemonade in the jug to start with was 5x.
Step 2: Another 15th of the amount in each container is poured into them.
This means that 1/15th of the current amount in each container is added to itself. So, the amount in the cup becomes x + x/15, and the amount in the jug becomes 5x + 5x/15.
Step 3: The amount of lemonade in the jug was then 3 times the amount in the cup.
So, we can set up the equation:
5x + 5x/15 = 3(x + x/15)
Step 4: Solve the equation to find x.
First, let's simplify the equation:
5x + (5/15)x = 3(x + (1/15)x)
5x + (1/3)x = 3x + (1/5)x
15x + 5x/3 = 9x + x/5
To eliminate the fractions, we can multiply both sides of the equation by 15*3*5 = 225:
225(15x + 5x/3) = 225(9x + x/5)
3375x + 225(x/3) = 2025x + 45x/5
3375x + 75x = 2025x + 9x
3450x = 2034x
3450x - 2034x = 0
1416x = 0
Step 5: Solve for x.
Divide both sides of the equation by 1416:
x = 0
Step 6: Calculate the initial amount in the jug.
Since the amount in the cup is 0 (x = 0), the initial amount in the jug is 5x = 5 * 0 = 0.
Therefore, there was no lemonade in the jug to begin with.