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Naiakea Special Education
Warm-up Problem
Toshi, a bird-watcher, saw a group of birds. He noticed the following:
There were 4 types of birds.
Two-sevenths of the group were sparrows.
Three-fifths of the rest were mynahs.
One-half of the birds that were neither sparrows nor mynahs were cardinals.
All the rest were doves; there were four doves
How many mynahs did Toshi see?
Hilo-Waiakea Special Education

Naiakea Special Education $\newline$ Warm-up Problem $\newline$ Toshi, a bird-watcher, saw a group of birds. He noticed the following: $\newline$ There were $4$ types of birds. $\newline$ Two-sevenths of the group were sparrows. $\newline$ Three-fifths of the rest were mynahs. $\newline$ One-half of the birds that were neither sparrows nor mynahs were cardinals. $\newline$ All the rest were doves; there were four doves $\newline$ How many mynahs did Toshi see? $\newline$ Hilo-Waiakea Special Education

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Percents of numbers: word problems

Full solution

Q. Naiakea Special Education

\newline

Warm-up Problem

\newline

Toshi, a bird-watcher, saw a group of birds. He noticed the following:

\newline

There were

4

types of birds.

\newline

Two-sevenths of the group were sparrows.

\newline

Three-fifths of the rest were mynahs.

\newline

One-half of the birds that were neither sparrows nor mynahs were cardinals.

\newline

All the rest were doves; there were four doves

\newline

How many mynahs did Toshi see?

\newline

Hilo-Waiakea Special Education

Assume total number of birds: Let's assume the total number of birds is $x$ .
Calculate sparrows: Calculate the number of sparrows, which is two-sevenths of the group. $\newline$ Sparrows = $(\frac{2}{7}) \times x$
Find birds not sparrows: Find the number of birds that are not sparrows. $\newline$ Not sparrows = $x$ - Sparrows $\newline$ Not sparrows = $x - (\frac{2}{7}) \times x$
Calculate mynahs: Calculate the number of mynahs, which is three-fifths of the birds that are not sparrows. $\newline$ Mynahs = $(\frac{3}{5}) \times \text{Not sparrows}$ $\newline$ Mynahs = $(\frac{3}{5}) \times (x - (\frac{2}{7}) \times x)$
Calculate birds neither sparrows nor mynahs: Calculate the number of birds that are neither sparrows nor mynahs. $\newline$ Neither = Not sparrows - Mynahs $\newline$ Neither = $(x - (\frac{2}{7}) \cdot x) - (\frac{3}{5}) \cdot (x - (\frac{2}{7}) \cdot x)$
Calculate cardinals: Half of the birds that are neither sparrows nor mynahs are cardinals. $\newline$ Cardinals = $(\frac{1}{2}) \times \text{Neither}$ $\newline$ Cardinals = $(\frac{1}{2}) \times ((x - (\frac{2}{7}) \times x) - (\frac{3}{5}) \times (x - (\frac{2}{7}) \times x)))$
Determine number of doves: The rest of the birds are doves, and there are $4$ doves. $\newline$ Doves $= 4$
Set up equation for x: Set up the equation to find x using the information about doves. $\newline$ Doves $=$ Neither - Cardinals $\newline$ $4 = ((x - (\frac{2}{7}) \cdot x) - (\frac{3}{5}) \cdot (x - (\frac{2}{7}) \cdot x)) - (\frac{1}{2}) \cdot ((x - (\frac{2}{7}) \cdot x) - (\frac{3}{5}) \cdot (x - (\frac{2}{7}) \cdot x))$

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