- WELCOME TO TWO EXAMPLES OF PROPORTION APPLICATIONS.
AS A NURSE, PART OF YOUR DAILY DUTIES IS TO MIX MEDICATIONS
IN THE PROPER PROPORTIONS FOR YOUR PATIENTS.
FOR ONE PATIENT YOU ALWAYS MIX MEDICATION "A" WITH MEDICATION B
IN THE SAME PROPORTION.
LAST WEEK YOUR PATIENT'S DOCTOR INDICATED
THAT YOU SHOULD MIX 60 MILLIGRAMS OF MEDICATION "A"
WITH 48 MILLIGRAMS OF MEDICATION B.
NOTICE THE RATIO OF MEDICATION "A" TO MEDICATION B
WOULD BE 60 TO 40.
HOWEVER, THIS WEEK THE DOCTOR SAID TO USE
40 MILLIGRAMS OF MEDICATION B.
THE QUESTION IS HOW MANY MILLIGRAMS OF MEDICATION "A"
SHOULD BE MIXED THIS WEEK.
TO SET UP OUR PROPORTION WE'LL SET UP TWO RATIOS
COMPARING THE AMOUNT OF MEDICATION "A"
TO THE AMOUNT OF MEDICATION B.
SO LAST WEEK THE RATIO WAS 60 MILLIGRAMS TO 48 MILLIGRAMS
FOR THE RATIO OF MEDICATION "A" TO MEDICATION B.
SO WE'LL HAVE THE RATIO OF 60 TO 48.
NOTICE THIS RATIO COMPARES THE AMOUNT OF MEDICATION "A"
TO MEDICATION B.
SO THE SECOND RATIO MUST BE IN THE SAME ORDER.
AND SINCE THIS WEEK WE'RE TOLD TO USE 40 MILLIGRAMS
OF MEDICATION B
40 MUST BE IN THE DENOMINATOR
AND THE NUMERATOR, OR THE AMOUNT OF MEDICATION "A,"
IS THE UNKNOWN WHICH WE'LL CALL "A."
AND NOW TO SOLVE FOR "A" WE CAN CROSS MULTIPLY
WHICH MEANS 48 x "A" MUST EQUAL 60 x 40.
SO 48 x "A" OR 48A MUST EQUAL 60 x 40 = 2,400.
SOLVE FOR "A" WE DIVIDE BOTH SIDES BY 48.
SO "A" = 2,400 DIVIDED BY 48 = 50.
SO THIS WEEK YOU NEED 50 MILLIGRAMS OF MEDICATION "A."
LET'S LOOK AT A SECOND EXAMPLE.
SUPPOSE YOU WORK FOR A LARGE COFFEE DISTRIBUTOR
THAT HAS A SECRET COFFEE BLEND THAT SELLS TO LOCAL STORES.
YOU MIX ORGANIC COFFEE WITH SUN CITY COFFEE
BUT ALWAYS IN THE SAME PROPORTION.
YESTERDAY YOU MIXED 80 POUNDS OF ORGANIC COFFEE
WITH 32 POUNDS OF SUN CITY COFFEE.
TODAY THERE IS 70 POUNDS OF ORGANIC COFFEE LEFT IN STOCK.
HOW MANY POUNDS OF SUN CITY COFFEE SHOULD YOU MIX WITH IT
TO GET YOUR SECRET BLEND?
AGAIN, WE'RE GOING TO SET UP TWO RATIOS.
THE RATIOS WILL COMPARE THE AMOUNT OF ORGANIC COFFEE
TO THE AMOUNT OF SUN CITY COFFEE.
SO THE FIRST RATIO WOULD BE 80 POUNDS TO 32 POUNDS OR 80 TO 32.
AGAIN, THIS IS COMPARING ORGANIC TO SUN CITY.
SO TODAY THERE IS 70 POUNDS OF ORGANIC.
SO THE 70 POUNDS HERE MUST GO IN THE NUMERATOR
OF THE SECOND RATIO
AND THE UNKNOWN IS THE AMOUNT OF SUN CITY COFFEE
WHICH WE'LL REPRESENT AS A VARIABLE.
LET'S USE S.
AND NOW WE CAN CROSS MULTIPLY TO SOLVE FOR S.
SO 80 x S = 32 x 70.
SO 80S = 32 x 70 = 2,240.
AND NOW TO SOLVE FOR S WE'LL DIVIDE BOTH SIDES BY 80.
SO S, THE AMOUNT OF SUN CITY COFFEE, WE NEED
WHEN USING 70 POUNDS OF ORGANIC COFFEE
IS EQUAL TO THIS QUOTIENT 2,240 DIVIDED BY 80 = 28.
SO THE ANSWER IS YOU NEED 28 POUNDS OF SUN CITY COFFEE.
I HOPE YOU FOUND THESE TWO EXAMPLES HELPFUL.