Question

3. Ketin's card collection is made up of baseball cards and footbal cards. The ratio of baseball cards to football cards is 6 to 7. He has 120 baseball cards. How many cards are in Kerin's card collection? Show your work.

Answer 1

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

`\begin{gathered} b\colon f=6\colon7 \\ (b)/(f)=(6)/(7) \\ \text{cross multiplying, we have } \\ 7* b=6* f \\ 7b=6f \\ \text{dividing both sides by 7 to get b, we have } \\ (7b)/(7)=(6f)/(7) \\ b=(6f)/(7) \end{gathered}`

Also, he has 120 baseball cards.

This means

`\begin{gathered} b=120 \\ \text{but } \\ b=(6f)/(7) \\ \text{That means that } \\ b=(6f)/(7)=120 \\ So,\text{ } \\ (6f)/(7)=120 \\ (6f)/(7)=(120)/(1) \\ \text{cross multiplying, we have } \\ 6f=120*7 \\ \text{dividing by 6, we have } \\ f=(120*7)/(6) \\ 120\text{ divided by 6 = 20, we have } \\ f=20*7 \\ f=140 \end{gathered}`

So, the total number of cards in Ketin's card collection is

`120+140=260`

Hence the answer is 260