Answer:
9 : 2
Step-by-step explanation:
The ratio of football to baseball cards is 3 : 2.
The ratio of baseball to basketball cards is 3 : 1.
To find the ratio of football to basketball cards, we need to determine a combined ratio. To do this, we aim to establish a common number of baseball cards in both ratios.
In the first ratio, the number of baseball cards is 2, while in the second ratio, it is 3. The lowest common multiple of 2 and 3 is 6. Therefore, we need to adjust the first ratio by multiplying it by 3 and the second ratio by 2:
The adjusted ratio of football to baseball cards is:
[tex]\textsf{Football}:\textsf{Baseball}=3 \times 3 : 2 \times 3 = \boxed{9 : 6}[/tex]
The adjusted ratio of baseball to basketball cards is:
[tex]\textsf{Baseball}:\textsf{Basketball}=3 \times 2 : 1 \times 2 = \boxed{6 : 2}[/tex]
Now we can combine the adjusted ratios to give the overall ratio of football to baseball to basketball cards:
[tex]\textsf{Football}:\textsf{Baseball}:\textsf{Basketball}=9 : 6 : 2[/tex]
Hence, the ratio of football to basketball cards is 9 : 2.
