Question

With a 5 to 7 ratio of Black Keys to white keys how many keys are black if the total is 240 keys

Answer 1

Let B and W represent the number of black and white keys, respectively.

Since the ratio of black keys to white keys is 5 to 7, then:

`(B)/(W)=(5)/(7)`

Additionally, since there is a total of 240 keys, then:

`B+W=240`

Isolate W from the first equation and substitute the value in the second equation to be able to solve for B:

`\begin{gathered} (B)/(W)=(5)/(7) \\ \Rightarrow W=(7)/(5)\cdot B \end{gathered}`
`\begin{gathered} B+W=240 \\ \Rightarrow B+(7)/(5)B=240 \\ \Rightarrow(12)/(5)B=240 \\ \Rightarrow B=(5)/(12)\cdot240 \\ \Rightarrow B=100 \end{gathered}`

Therefore, there are 100 black keys.