- SUPPOSE YOU WORK
FOR A LARGE COFFEE DISTRIBUTOR
THAT HAS A SECRET BLEND
IT SELLS TO LOCAL STORES.
YOU MIX THE RIFT VALLEY BLEND
WITH THE BREAKFAST BLEND,
BUT ALWAYS
IN THE SAME PROPORTION.
YESTERDAY YOU MIXED 60 POUNDS
OF THE RIFT VALLEY BLEND
WITH 18 POUNDS
OF THE BREAKFAST BLEND.
TODAY THERE ARE ONLY 40 POUNDS
OF THE RIFT VALLEY COFFEE
LEFT IN STOCK.
HOW MANY POUNDS
OF THE BREAKFAST COFFEE
SHOULD YOU MIX WITH IT
TO GET YOUR SECRET BLEND?
SO I'LL SOLVE THIS PROBLEM
USING A PROPORTION
WHERE WE SET UP TWO RATIOS
COMPARING THE AMOUNT
OF RIFT VALLEY BLEND
TO THE AMOUNT
OF BREAKFAST BLEND.
SO FOR THE FIRST RATIO,
BECAUSE YOU MIX 60 POUNDS
OF THE RIFT VALLEY BLEND
WITH 18 POUNDS OF
THE BREAKFAST BLEND,
OUR FIRST RATIO WILL BE 60:18.
NOTICE HOW THIS RATIO
IS COMPARING
THE AMOUNT OF RIFT VALLEY TO
THE AMOUNT OF BREAKFAST BLEND.
AND THEREFORE THE SECOND RATIO
MUST BE SET UP IN THE SAME WAY.
SO TODAY THERE ARE
ONLY 40 POUNDS
OF THE RIFT VALLEY COFFEE,
SO THE 40 WOULD GO ON TOP.
AND THE QUESTION ASKS HOW MANY
POUNDS OF BREAKFAST BLEND
WOULD BE NEEDED
TO KEEP THE SAME MIX.
SO THE AMOUNT OF THE BREAKFAST
BLEND HERE IS UNKNOWN,
WHICH WE'LL LET BE EQUAL TO X.
NOW THAT WE HAVE A PROPORTION,
WE CAN CROSS-MULTIPLY
AND SOLVE FOR X.
WHEN WE CROSS-MULTIPLY, WE'LL
HAVE 60 x X MUST EQUAL 18 x 40.
SO 60 x X = 60X = 18 x 40.
18 x 40 = 720.
SO WE HAVE 60X = 720.
AND NOW TO SOLVE FOR X,
WE DIVIDE BOTH SIDES BY 60.
NOTICE ON THE LEFT SIDE HERE,
60 DIVIDED BY 60
SIMPLIFIES TO 1.
1 x X IS JUST X.
ON THE RIGHT SIDE WE HAVE
720 DIVIDED BY 60,
WHICH IS EQUAL TO 12.
WHICH MEANS IF YOU HAVE 40
POUNDS OF RIFT VALLEY COFFEE
AND YOU WANT TO MAKE
THE SECRET BLEND CORRECTLY,
YOU NEED TO MIX IT WITH 12
POUNDS OF THE BREAKFAST BLEND.
I HOPE YOU FOUND THIS HELPFUL.
