Let  represent the number of liters of the 40% solution. Then it follows that  liters of the 40% solution plus 4 liters of the 10% solution will equal (x+4) liters of a 25% solution. This can be represented by the following equation:

Now solve for x:

You will need 4 liters of the 40% solution in order to make a mixture that is 25% alcohol by volume

To begin, notice that there is a  ratio between the water in your container and the water specified by the mix of the components.  Given that there are  total parts in your solution, this means that you can set up this equation:

Multiplying both sides by 8, you get:

There are  total gallons of solution.

To begin, you know that the basic form of the solution has a total of , or  parts.  Now, we know that we are going to have to add  parts of orange juice.  This means that the new solution will have  parts orange juice and  total parts (since we are adding to the original).  Since we want this to be % orange juice, we really want the following equation to be true:

Solve the following equation, therefore:

Multipy by :

Now, isolate :

First, add up the four parts of the ratio. This equals 25 parts. These 25 parts make up the 75 pound mixture, which means the 75 pound mixture is composed of 3 times the 25 parts (25x = 75 so x = 3).

This allows you to know that the number of pounds of chocolate chips is 3 times the ratio, i.e. 3 * 5 = 15. The mixture includes 15 pounds of chocolate chips. The answer is 15.

The best approach is to add the numerator and denominator of the ratio (5 + 1 = 6), and then divide the total by that sum (120/6 = 20). This gives you the value for 1 part when the total is divided into 6 parts and, luckily for us, there is only 1 part women for every 5 parts men. Now set up equal ratios: men/women = 5/1 = x/20. Solve for the number of men by cross multiplying (5 * 20 = 1x). So there are 100 men and 20 women, which makes 80 more men than women.

If 2/3 is cut off and thrown away, that means 1/3 of the original length remains. Of this, 1/4 gets cut off and thrown away, meaning 3/4 of 1/3 still remains. Multiplying 3/4 * 1/3, we get 1/4.

Answer: 25
Explanation: For this type of problem, build an equation that represents the relationships between the quantities and solve for the quantitiy you need. The problem states that b=1/4c and a = 1/3b. Thus, a = 1/3(1/4)c, or 1/12 of c. Now put everything in terms of c, thus 1/12c + 1/4c +c = 400. Now comes the tricky step--combine like terms and create the improper fraction (1/12c + 3/12c + 12/12c = 16/12c). Reduce the fraction to 4/3. So 400 is 4/3 of c. Thus c is 3/4 of 400, or 300. a is 1/12 of 300, or 25.

Since she spent 1/4 on the ticket, 3/5 of the remaining 3/4 of the money was spent on popcorn: 3/5 x 3/4 = 9/20.  This means 9/20 of the money was spent on popcorn so in total: 1/4 + 9/20 = 14/20 = 7/10 of her money was spent.  This leaves 3/10 of her money behind: 3/10x 10 = 3.00.

Set up a proportion: 18.50/5 = x/2.  Cross multiply and solve for x: 37 = 5x.... x = 7.40.

It's tempting to pick 1 hour, but that is a trick answer! Picture 3 men each painting 1 room. All 3 of the rooms are done after 3 hours, so each man actually spends 3 hours painting his room, not 1 hour.