Question

i was waking in a park yesterday when suddenly i heard lovely music comming for the ground. I gasped when I looked down because I saw 442 ants a beetles having a concert ¾ of the number of ants was equal to ⅓ of the number of beetles. how many ants did I see?

Answer 1

Let A be the number of ants and B be the number of beetles. It is given that ¾ of the number of ants was equal to ⅓ of the number of beetles.

So, we can write,

`\begin{gathered} (3)/(4)A=(1)/(3)B \\ (A)/(B)=(4)/(3*3) \\ \text{ }(A)/(B)\text{ }=(4)/(9) \end{gathered}`

Now, let A=4x and B=9x, where x is a constant.

There was a total of 442 ants and beetles. So,

A+B=442.

Hence, we can write

`\begin{gathered} A+B=4x+9x \\ \text{ }A+B\text{ =13x} \\ \text{ 442=13x} \\ (442)/(13)=x \\ 34=x \end{gathered}`

Since the number of ants is 4x, we can write

`4x=4*34=136`

Therefore, the number of ants is 136.