Question

The ratio of the number of sparrows visiting a bird feeder to the number of more interesting birds is 3.88. On a morning when altogether 109 birds visit the feeder, what is the number of sparrows?

Answer 1

We know that the ratio between sparrows and the other birds is 3.88. Let x be the number of sparrows and y be the number of the other birds, then we have that:

$\frac{x}{y}=3.88$

We know that the total number of birds is 109, then:

$x+y=109$

solving the second equation for y we have:

$y=109-x$

Plugging this in the first equation and solving for x we have:

$\begin{gathered} \frac{x}{109-x}=3.88 \\ x=3.88(109-x) \\ x=422.92-3.88x \\ x+3.88x=422.92 \\ 4.88x=422.92 \\ x=\frac{422.92}{4.88} \\ x=86.66 \end{gathered}$

Therefore approximately 87 sparrows were in the feeder that morning. (We round up the number since we can't have a fraction of a sparrow)