Linear equations word problems
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Linear equation word problem: sugary drinks
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.