Hawaiiain punch is 10% fruit juice. How much water would you have to add to one gallon of hawaiiain punch to get a drink that is 6% fruit juice?
my homework is 1 thru 41 odd, been able to solve all but #39. on the above I cannot figure out how to set it up. Thank you in advance for any help
First I'll give you the answer and check it. Then I'll tell
you how I got it. The reason I do it this way is to show
you that it takes the exact same thinking to check a word
problem, starting with the answer, as it does to set up the
equation, starting with x. You'll see.
The answer: You would have to add of a gallon of water.
Checking using the answer gallon of water.
We have 1 gallon of Hawaiian punch to begin with.
10% of 1 gallon is gallon of fruit juice.
Suppose we add gallon of water. We will then
have or gallons of liquid of
which gallon is fruit juice, so
equals
because = = =
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Now if you understand that, we will now "check it" using gallon:
"Checking" using gallon of water.
We have 1 gallon of Hawaiian punch to begin with.
10% of 1 gallon is gallon of fruit juice.
Suppose we add gallon of water. We will then
have gallons of liquid of
which gallon is fruit juice, so
equals
or
=
Multiply both sides by
=
Multiply both sides by 10
=
Multiply both sides by 10
=
=
Subtract 6 from both sides:
=
Divide both sides by 6
=
Simplifying:
=
Edwin