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# Linear equation word problem: sugary drinks

Sal solves the following problem: Drink A with 40% sugar is mixed with Drink B to obtain Drink C which has 25% sugar. What is the percentage of sugar of Drink B? Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

Make a table and solve. A biologist is researching the
impact of three different water-based sugar drinks on bees
ability to make honey. He takes 2 liters of Drink A,
which contains 40% sugar. So let me write this down. Let me make our table and
then we can solve it. So let's take amount of drink. And then we'll say
percent sugar. And then we can say sugar
quantity, so the actual physical quantity of sugar. Maybe I should say sugar amount,
or amount of sugar. Now this first drink, Drink A,
it says he takes 2 liters of Drink A, which contains
40% sugar. The first column will be which
drink we're talking about, so Drink A, he takes
2 liters of it. It's 40% sugar. So if we want the actual amount
of sugar in liters, we just multiply 2 liters times
40%, or times 0.4. Let me write times with a dot so
you don't think it's an x. 2 times 0.4, which is equal
to 0.8 liters of sugar. So you have 0.8 liters
of sugar. 1.2 liters of I guess the other
stuff in there is water. But it's 0.8 of the 2 liters
is sugar, which is 40%. Now,, he adds 1.2 liters
of Drink B. He finds that bees prefer this
new solution, Drink C. So when you add these two
together, you end up with Drink C. And we end up with how
much of Drink C? 2 plus 1.2 is 3.2 liters
of Drink C, which has 25% sugar content. So this is 25% sugar, which also
says we know the amount of sugar in it. Because if we have 3.2 liters
of it and it's 25% sugar, or it's 1/4 sugar, that means that
we have 0.8 liters of sugar here. So this is 0.8 liters
of sugar. Well, that I already wrote
in the column name. That's the amount of sugar. It's 25% sugar. We have 3.2 liters of it. Now, they want to know what
is the percentage of sugar in Drink B? So let's just call that x. So that's right over here. Now, if it's x percent sugar
here, or this is the decimal equivalent, that's x, how
much sugar do we have? We have 1.2 liters times the
decimal equivalent of sugar, so this is going to
be 1.2 times x. Now let's think about it. We have 0.8 liters of sugar in
Drink A, and when you add this amount to it, you still have
0.8 liters of actual sugar in Drink C. So this thing has to
be equal to zero. We could set up an
equation here. We could write 0.8 plus
1.2x is equal to 0.8. You subtract 0.8 from
both sides. You get 1.2x is equal to 0. x
has got to be equal to 0. So this thing right here
has got to be zero. There's no sugar in Drink B. It's just got to be
like 1.2 liters. I guess the solution is water. So it's 1.2 liters of water. There's no sugar in Drink B. It is 0% sugar.