QuestionA bottle has $0.068 \mathrm{~L}$ of cough syrup. If 5 mL is taken 4 times daily, how many days until a refill?

Studdy Solution

STEP 1

Assumptions1. The bottle contains0.068 L of cough syrup. One dose is one teaspoon, which is equivalent to5 mL3. Four doses are given each day

STEP 2

First, we need to convert the volume of the cough syrup from liters to milliliters, as the dosage is given in milliliters. We can do this by using the conversion factor1 L =1000 mL.
$Volume\, in\, mL = Volume\, in\, L \\times1000$

STEP 3

Now, plug in the given value for the volume in liters to calculate the volume in milliliters.
$Volume\, in\, mL =0.068\, L \\times1000$

STEP 4

Calculate the volume in milliliters.
$Volume\, in\, mL =0.068\, L \\times1000 =68\, mL$

STEP 5

Now that we have the volume in milliliters, we can find the total number of doses in the bottle. This can be done by dividing the total volume by the volume of one dose.
$Total\, doses = Volume\, in\, mL / Volume\, of\, one\, dose$

STEP 6

Plug in the values for the volume in milliliters and the volume of one dose to calculate the total number of doses.
$Total\, doses =68\, mL /5\, mL$

STEP 7

Calculate the total number of doses.
$Total\, doses =68\, mL /5\, mL =13.6$

STEP 8

Since we cannot have a fraction of a dose, we round down to the nearest whole number. This gives us the total number of full doses in the bottle.
$Total\, full\, doses =13$

STEP 9

Now that we have the total number of full doses, we can find the number of days before a refill is needed. This can be done by dividing the total number of doses by the number of doses given each day.
$Days\, before\, refill = Total\, full\, doses / Doses\, per\, day$

STEP 10

Plug in the values for the total number of full doses and the number of doses per day to calculate the number of days before a refill is needed.
$Days\, before\, refill =13 /4$

STEP 11

Calculate the number of days before a refill is needed.
$Days\, before\, refill =13 /4 =3.25$

STEP 12

Since we cannot have a fraction of a day, we round up to the nearest whole number. This gives us the number of full days before a refill is needed.
$Full\, days\, before\, refill =4$ A refill is needed after4 days.

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