# Peggy Sue decided to enter her famous chili at her local chili cooking contest. Normally, she needs five tomatoes to make enough chili for her family of seven famous recipe. How many tomatoes should she expect to use to make her for 100 people?

Oct 22, 2016

72 tomatoes.

#### Explanation:

You can do it two ways:

Method 1: Find the number of tomatoes needed for one person.

If five tomatoes are needed to make enough chilli for seven people, then $\frac{5}{7}$ tomatoes are needed for one person.

To find the number of tomatoes for one hundred people, simply multiple $\frac{5}{7}$ by 100.

$\frac{5}{7} \cdot 100 = 71.4285 \ldots$

Since you can't have 71.4 tomatoes, simply round up to the nearest whole number to get 72 tomatoes.

Method 2: Find out how many sevens go into one hundred and multiply that number by five to get the number of tomatoes needed.

$\frac{100}{7} = 14.285714286$

$14.285714286 \cdot 5 = 71.4285 \ldots$

Again, round up to the nearest whole number because you can't have 71.4 tomatoes.

Oct 22, 2016

It is astonishing just how much ratio is the underlying principle behind many calculations.

72 tomatoes

#### Explanation:

Using ratio in fraction format giving:" "("tomato count")/("people count")

Let the count of tomatoes for 100 people be $x$

$\left(\text{tomato count")/("people count}\right) \to \frac{5}{7} \equiv \frac{x}{100}$

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$\textcolor{b l u e}{\text{Method 1}}$

Multiply both sides by 100

$\frac{5}{7} \times 100 = \frac{x}{100} \times 100$

$\frac{5 \times 100}{7} = \frac{x \times 100}{100}$

$\frac{500}{7} = x \times \frac{100}{100} \text{ "color(red)(->5xx100/7=x" "larr"see method two}$

$x = 71 \frac{3}{7} \text{ tomatoes exactly}$

As you would not have part of a tomato we have 72
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Method 2") color(red)(" "larr" Shows why method 1 works"

$\frac{5}{7} = \frac{x}{100}$

We need to change the 7 into 100. This is achieved by multiplying by $\frac{100}{7}$. To maintain the ratio you would need to multiply both top and bottom (numerator and denominator) by the same value. So we have:

$\frac{5}{7} \text{ "=" "x/100" " ->" } \frac{\textcolor{red}{5 \times \frac{100}{7}}}{7 \times \frac{100}{7}} = \frac{\textcolor{red}{71 \frac{3}{7}}}{100}$