# Question 1ca5a

Apr 29, 2016

Here's what I got.

#### Explanation:

These are classic examples of unit conversion problems that can be solved by using one or more conversion factors that help you go from one unit to another.

As far as I know, the most common conversion factor used to convert between milliliters to drops and vice versa is

$\textcolor{p u r p \le}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 mL " = " 20 drops}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

This tells you that in order to have $\text{1 mL}$ of soda, you need to have $20$ drops of soda. Since you know that a can of soda contains $\text{355 mL}$ of liquid, you can use this conversion factor to determine how many drops would be needed to get that volume

$355 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{mL soda"))) * "20 drops"/(1color(red)(cancel(color(black)("mL soda")))) = color(green)(|bar(ul(color(white)(a/a)"7100 drops} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The exact same approach can be used to determine how many bales of hay will be consumed in one year. Unless the problem says otherwise, you can usually approximate one year to be equivalent to $52$ weeks

$\textcolor{p u r p \le}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 year " = " 52 weeks}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

This time, you know that the herd consumes $14$ bales of hay in $2$ weeks, which is equivalent to saying that they consume

1 color(red)(cancel(color(black)("week"))) * "14 bales of hay"/(2color(red)(cancel(color(black)("week")))) = "7 bales of hay"

in one week. Since you need $52$ weeks to get to one year, it follows that the heard will consume $52$ times more hay in one year than it does in one week.

7color(white)(a) "bales of hay"/(1color(red)(cancel(color(black)("week")))) * (52color(red)(cancel(color(black)("weeks"))))/"1 year" = color(green)(|bar(ul(color(white)(a/a)"364 bales of hay/year"color(white)(a/a)|)))#