Question

1 mL = 32 drops from a dropper. If a 15 mL container holds 60 equal doses of medicine, how many drops are in a dose?

Answer 1

`"8 drops " = " 1 dose"`

Explanation:

The problem tells you that every milliliter of the container is equivalent to `32` drops of medicine, which basically means that you are given a conversion factor that takes you from milliliters to drops or vice versa.

You can calculate the number of drops present in the container by keeping in mind that the milliliters to drops ratio must be constant

`"no. of milliliters"/"number of drops" = "constant" = 1/32`

If you take `x` to be number of drops in the `"15 mL"` container, you will have

`"1 mL"/"32 drops" = "constant" = "15 mL"/x`

This means that you have

`x = ("32 drops" xx 15 color(red)(cancel(color(black)("mL"))))/(1color(red)(cancel(color(black)("mL")))) = "480 drops"`

Now all you have to do is use the fact that the container holds `60` doses of medicine, the equivalent of `480` drops, to find the number of drops needed to have a dose of medicine.

`"60 doses"/"480 drops" = "1 dose"/y`

You will have

`y = ("480 drops" xx 1 color(red)(cancel(color(black)("dose"))))/(60color(red)(cancel(color(black)("doses")))) = "8 drops"`

Therefore, you need `8` drops to have `1` dose of medicine.