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Question 255188: If you mix fruit juice and bubbly water in a ratio of 3 to 5 to make a punch then how many liters of juice and how many liters of bubbly water will you need to make 24 liters. Please explain with a strip diagram.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f = number of liters of fruit juice.
b = nume of liters of bubbly water.
ratio f/b = 3/5
total liters = 24.
your equation is f + b = 24.
since f/b = 3/5, thie means that:
f = 3b/5
equation of f + b = 24 becomes:
3b/5 + b = 24
multiply both sides of this equation by 5 to get:
3b + 5b = 120 which becomes:
8b = 120 which becomes:
b = 120/8 = 15.
since f + b = 24, this means that f = 24-15 = 9.
you have f = 9 and b = 15
f + b = 9 + 15 = 24
f/b = 9/15 = 3/5
ratio holds and the sum is correct.
if you used a strip diagram, you might do the following:
let 1 strip represent 3 liters of fruit juice.
this strip would be divided into 3 equal sections.
let another strip represent 5 liters of bubbly water.
this strip would be divided into 5 equal sections.
each section would represent 1 liter.
first strip would look like fff
second strip would look like bbbbb
since the ratio has to remain constant, then combine these strips into one long strip that is composed of 3 sections of f and 5 sections of b.
that would look like:
fffbbbbb = 8 liters.
since you want 24 liters, how many times does this strip divide into 24.
answer is 3.
you get:
fffbbbbb + fffbbbbb + fffbbbbb = 24 liters.
add up the f's and you get 9.
add up the b's and you get 15.
you have 9 liters of fruite juice and 15 liters of bubbly water to make a total of 24 liters of mixture.
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