Eric, John and Tony have 105 stickers altogether. John has twice as many stickers as Tony, while Eric has twice as many stickers as John.
a) How many stickers does Eric have?
b) How many stickers must Tony receive from Eric, so that all three boys have the same number of stickers?
Let's assign variables to the number of stickers each boy has:
Let x be the number of stickers Tony has.
John has twice as many, so he has 2x stickers.
Eric has twice as many as John, so he has 2 * 2x = 4x stickers.
Together they have x + 2x + 4x = 7x stickers.
We know that altogether they have 105 stickers, so 7x = 105.
Dividing both sides of the equation by 7, we get x = 105 / 7 = <<105/7=15>>15.
a) Eric has 4x = 4*15 = <<4*15=60>>60 stickers.
b) To have the same number of stickers, Tony must receive 60 - x = 60 - 15 = <<60-15=45>>45 stickers from Eric. Answer: \boxed{45}.
Let's solve this step-by-step:
Step 1: Let's assume the number of stickers Tony has as "x".
Step 2: According to the given information, John has twice as many stickers as Tony. Therefore, John has 2x stickers.
Step 3: Similarly, Eric has twice as many stickers as John. Therefore, Eric has 2 * (2x) = 4x stickers.
Step 4: Now, let's add the number of stickers for all three boys together. Tony has x stickers, John has 2x stickers, and Eric has 4x stickers. The total is x + 2x + 4x = 7x.
Step 5: We know that the total number of stickers for all three boys is 105. Therefore, we can set up the equation 7x = 105.
Step 6: To find the value of x, we can divide both sides of the equation by 7. This gives us x = 105 / 7 = 15.
Step 7: Now that we know the value of x, we can substitute it back into the equations for John and Eric to find the number of stickers each has.
a) Eric has 4x stickers, substituting x = 15, we get: Eric has 4 * 15 = 60 stickers.
b) To find how many stickers Tony must receive from Eric so that all three boys have the same number of stickers, we need to find the common number of stickers.
Since Eric has 60 stickers, Tony needs to receive 60 - x stickers from him, where x = 15. Therefore, Tony needs to receive 60 - 15 = 45 stickers from Eric.