Juan and Will each had a collection of puppets. Will had 2/7 as many stickers as Juan. When Juan lost 24 stickers, Will then had twice as many as Juan. How many stickers were in Juan's collection at first?
To solve this problem, let's break it down into steps:
Step 1: Set up a variable:
Let's assume the number of stickers in Juan's collection at first is "x".
Step 2: Calculate the number of stickers Will had initially:
Since it is given that Will had 2/7 as many stickers as Juan, we can calculate the number of stickers Will had as (2/7) * x.
Step 3: Calculate the number of stickers Juan had after losing 24 stickers:
After Juan lost 24 stickers, the number of stickers he had left is (x - 24).
Step 4: Set up an equation:
It is given that Will then had twice as many stickers as Juan. We can express this as the equation: (2/7) * x = (x - 24)
Step 5: Solve the equation:
Multiply both sides of the equation by 7 to eliminate the fraction: 2x = 7(x - 24).
Expand and simplify: 2x = 7x - 168.
Subtract 7x from both sides: -5x = -168.
Divide both sides by -5 to solve for x: x = 33.6
Step 6: Final answer:
Juan initially had 33.6 stickers in his collection. However, since the number of stickers cannot be a fraction, we round it to the nearest whole number. Therefore, Juan had 34 stickers in his collection at first.
So, the answer is 34 stickers.