Since  and  are being set to numbers of milliliters, we convert one liter to 1,000 milliliters. The sum of the amounts of the two solutions  and  is 1,000, so

is one equation of the system.

The other equation will add the acid. The amount of acid in an acid solution is the concentration, as a decimal, multiplied by the amount of solution. The amount of acid in the pre-mixture solutions are  and ; add these to get the amount of acid in 1,000 milliliters of a 20% solution, or  milliliters:

The correct system is:

Since a normal batch of candies is one-sixth green candies, then it contains  pounds of green candies; the defective batch contained half this, or 5 pounds. If we let  be the number of pounds of green candies that were added, then, after the addition, there were  pounds of green candies in a batch of  candies. One sixth of the candies are green, so set and solve the equation:

Six pounds of green candies are added.

Initially, there were 48 pounds of candies. In a normal batch, one sixth of them, or  pounds, should be white, but in the defective batch, half this, or 4 pounds, were white. Subsequently, 44 pounds of candies in the defective batch were not white.

Let  be the number of pounds of candy in the batch after the white candies were added. Since  of a normal batch of candies are not white,  pounds of candies are not white; since no candies that weren't white were added, 

The closest choice, and the correct one, is 53 pounds.

First, we should find out what isn't water in the apple; let's call this the pulp. The pulp accounts for  of the weight of the fruit before being dried. Therefore, the pulp weighs . We can then express as a ratio the amount of pulp in the apple to the total weight of the fruit after it has been slightly dried as follows: 

We can rearrange this equation to yield: 

The weight of the water in the dried fruit is therefore . To this weight we simply add the weight of the pulp and we get the final answer, 

For the sake of simplicity, assume that each jar holds 100 milliliters of water - this reasoning is independent of the actual capacity. 

The first jar is 20% full, so it contains  milliliters of solution; this solution is 80% salt, so there are  millilters of salt in the solution. Similarly, the second jar includes  milliliters of solution, which include  milliliters of salt.

Therefore, when the two solutions are mixed, the concentration of salt will be

.

For the sake of simplicity, let us assume that each jar has capacity 100 milliliters; the reasoning is the same regardless of the common capacity. 

The first jar is 40% full, so there are  milliliters of solution in the jar; the solution is 60% salt, so there are  milliliters of salt in the solution. 

For the first jar to be filled to capacity,  milliliters of solution must be added. Also, if the solution is 30% salt, then the jar will contain milliliters of salt. This means that  milliliters of salt will have been added. This means that the concentration of salt in the added solution - the contents of the second jar - is

.

(Note that the actual size of the second jar does not matter.)

Let  be the number of pounds of Licorice Dream tea; then  is the number of pounds of Strawberry Explosion. Then the total value of each ingredient tea, as well as the total value of the new tea, will be:

Licorice:  or 

Strawberry:  or 

New tea: 

Add the individual costs of the ingredient teas to get the total cost of the new tea.

Charlie will use 15 pounds of the Licorice Dream; as this is not one of the given answers, the correct answer is "None of the answers are correct".

There are 36 possible outcomes (). 10 out of the 36 outcomes are greater than 8: (6 and 3)(6 and 4)(6 and 5)(6 and 6)(5 and 4)(5 and 5)(5 and 6)(4 and 5)(4 and 6)(3 and 6).

Since there are 300 people,  people play baseball and  of those people play both baseball and soccer. Therefore, there are  people who play baseball but not soccer.

Probability:

probability on one roll:

for both times=