# Of 3,600 students surveyed, 40% eat cold pizza for breakfast. How many students do not eat cold pizza for breakfast?

Jun 9, 2018

2,160 students

#### Explanation:

Use the proportion method to solve these:

$\frac{\text{part"/"whole"="part of 100}}{100}$

You want to solve, 40% is what part of 3,600:

$\frac{\text{part}}{3600} = \frac{40}{100}$

cross multiply:

$100 \cdot \text{part} = 40 \cdot 3600$

$100 \cdot \text{part} = 144000$

$\text{part} = \frac{144000}{100}$

$\text{part} = 1440$

It asks for the students that don't eat cold pizza so subtract this from the total:

$3600 - 1440 = 2160$

Jun 17, 2018

2160

#### Explanation:

$\textcolor{b l u e}{\text{Some reasoning about percent}}$

Splitting this word up into its component parts:

per $\to$ for each of
cent $\to$ 100

So for example 30 percent means that we select 100 of something and $\underline{\text{within}}$ that 100 we have 30 of what we are after.

Basically percentage is a fraction but as its name indicates the denominator is always fixed at 100.

There are two way of writing percentage. Each one means EXACTLY the same thing as the other. Sticking with the example of 30 percent. This can be written as 30% or as $\frac{30}{100}$

So we need to be able to mathematically go directly from one to the other.

$\frac{30}{100}$ can be written as $30 \times \frac{1}{100}$ This makes sense as we have a count of 30 and what we are counting has unit size of $\frac{1}{100}$ of something. Thus:

30 color(white)("dd.d")%
$\textcolor{w h i t e}{\text{dddd.d}} \uparrow$
$30 \textcolor{w h i t e}{\text{dd}} \overbrace{\times \frac{1}{100}}$

As the above are EXACTLY the same thing then % means $\times \frac{1}{100}$ including the multiply

Consequently when someone write: color(green)("some number" xx100% what they are really stating mathematically is:color(green)("some number" xx100/100
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answering the question}}$

If 40% eat pizza than (100-40)% = 60% do not eat pizza.

Thus we have: $\frac{60}{\cancel{100}} ^ 1 \times {\cancel{3600}}^{36} = \underbrace{6 \times 36 \times 10} = 2160$
$\textcolor{w h i t e}{\text{dddddddddddddddddddddddddddddd}} \textcolor{b r o w n}{\uparrow}$
$\textcolor{w h i t e}{\text{dddddddddddddddd")color(brown)("A trick for calculating it in your head}}$

Jun 17, 2018

$\textcolor{b l u e}{2160 \text{ Students}}$

#### Explanation:

If 40% eat cold pizza, then 60% don't.

60% of 3600.

$\frac{60}{100} \times 3600 = 2160$