SOLUTION
Let the total number of cards in Ketin's card collection be k
Let the number of baseball cards be b, and
the number of football cards be f
Now, the ratio of baseball cards to football cards is 6 to 7, that is
[tex]\begin{gathered} b\colon f=6\colon7 \\ \frac{b}{f}=\frac{6}{7} \\ \text{cross multiplying, we have } \\ 7\times b=6\times f \\ 7b=6f \\ \text{dividing both sides by 7 to get b, we have } \\ \frac{7b}{7}=\frac{6f}{7} \\ b=\frac{6f}{7} \end{gathered}[/tex]Also, he has 120 baseball cards.
This means
[tex]\begin{gathered} b=120 \\ \text{but } \\ b=\frac{6f}{7} \\ \text{That means that } \\ b=\frac{6f}{7}=120 \\ So,\text{ } \\ \frac{6f}{7}=120 \\ \frac{6f}{7}=\frac{120}{1} \\ \text{cross multiplying, we have } \\ 6f=120\times7 \\ \text{dividing by 6, we have } \\ f=\frac{120\times7}{6} \\ 120\text{ divided by 6 = 20, we have } \\ f=20\times7 \\ f=140 \end{gathered}[/tex]So, the total number of cards in Ketin's card collection is
[tex]120+140=260[/tex]Hence the answer is 260
