# if anthony had 3 times as many marbles as he actually has, he would have 1/3 as many marbles as Billy has. what is the ratio of the number of marbles Anthony has to the number of marbles Billy has?

a)1:9
b)1:3
c)1:1
d)3:1
e) 9:1

1:9
Ex: Anthony has 3 marbles and Billy has 27. 3 is 1/9 of 27, and if you triple 3, you get 9, which is 1/3 of 27.

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## The correct answer is a) 1:9.

Let's assume that Anthony has x number of marbles. According to the information given, if Anthony had 3 times as many marbles, he would have 3x marbles.
On the other hand, it is stated that Anthony would have 1/3 as many marbles as Billy has. Let's assume that Billy has y number of marbles. According to this, Anthony would have 1/3 of y marbles, which is (1/3)y.

Now we can set up an equation using the given information:
3x = (1/3)y

To make it easier to compare the marbles Anthony and Billy have, let's multiply both sides of the equation by 3:
9x = y

This equation shows that if Anthony had 3 times as many marbles, he would have the same number of marbles as Billy. Therefore, the ratio of the number of marbles Anthony has to the number of marbles Billy has is 1:9. So the correct answer is a) 1:9.

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## To solve this problem, we can set up an equation based on the given information.

Let's say Anthony has x marbles and Billy has y marbles. According to the question, if Anthony had 3 times as many marbles as he actually has, he would have 1/3 as many marbles as Billy has.

So, the equation can be written as:

3x = (1/3)y

To find the ratio of the number of marbles Anthony has to the number of marbles Billy has, we can simplify this equation.

Multiply both sides of the equation by 3 to eliminate the fraction:

9x = y

Now, we can express the ratio of the number of marbles Anthony has to the number of marbles Billy has as x:y. From the equation above, we can see that x = 1 and y = 9.

Therefore, the ratio of the number of marbles Anthony has to the number of marbles Billy has is 1:9.

So, the correct answer is (a) 1:9.