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QUESTION

# Pepsi puts 355 ml of pop in a can. How many drops is this?

Here's what I got.

These are classic examples of 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

color(purple)(|bar(ul(color(white)(a/a)color(black)("1 mL " = " 20 drops")color(white)(a/a)|)))

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

355 color(red)(cancel(color(black)("mL soda"))) * "20 drops"/(1color(red)(cancel(color(black)("mL soda")))) = color(green)(|bar(ul(color(white)(a/a)"7100 drops"color(white)(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

color(purple)(|bar(ul(color(white)(a/a)color(black)("1 year " = " 52 weeks")color(white)(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)|)))