To start this, you can set up a proportion as follows:

, where  is the number of cups of orange juice.

Now, solving for , you get:

Be careful, though! This means that the total solution is actually  or .

To start, notice that the ratio of solution X to solution Y is:

Based on the quesiton, you know that you are looking for a certain amount of solution X based on a given amount of solution Y. Thus, for your data, you know:

Solving for X, you get:

This is the total amount of solution X that you will need to keep the ratios correct. Do not forget that you need to have a total solution amount, thus add this amount of solution X to solution Y's amount, thus giving you:

 or 

Set up the proportions a/b = 9/2 and c/b = 5/3 and cross multiply.

2a = 9b and 3c = 5b.

Next, substitute the b’s in order to express a and c in terms of each other.

10a = 45b and 27c = 45b --> 10a = 27c

Lastly, reverse cross multiply to get a and c back into a proportion.

a/c = 27/10

Since there are 5 defective radios, there are 45 nondefective radios; therefore, the ratio of non-defective to defective is 45 : 5, or 9 : 1.

The ratio of green to blue is .

Without simplifying, the ratio of green to blue is  (order does matter).

Since 3 and 9 are both divisible by 3, this ratio can be simplified to .

Let  be the number of store employees,  the number of store managers, and  the number of corporate managers.

, so the number of store employees is .

, so the number of store managers is .

, so the number of corporate managers is .

Therefore, the number of employees who are either store managers or corporate managers is .

For this problem, we need to find the number of employees who fall into the categories described, keeping in mind that multiple portions of the pie chart must be accommodated for. Then, we can fit them into a ratio:

For the "2 to 9 years" portion of the financial industry, include

(0.2 + 0.18)(12,000,000) = 4,560,000 workers.

For the "0 to 4 years" portion of the construction industry, include

(0.15 + 0.2)(8,000,000) = 2,800,000 workers.

Now divide and simplify to find the ratio:

4,560,000/2,800,000 = 8/5.

Since the ratios are fixed, regardless of the actual values of , , or , we can let  and

In order to convert to a form where we can relate  to , we must set the coefficient of  of each ratio equal such that the ratio can be transferred. This is done most easily by finding a common multiple of  and  (the ratio of  to  and , respectively) which is

Thus, we now have  and .

Setting the  values equal, we get , or a ratio of 

First, begin by calculating the total number of each item that there will be at the end of the process.

Cups: 

Saucers: 

The ratio of cups to saucers will thus be:

In order to solve this problem, create an equation that summarizes the roof repair cost for each company. Begin by composing a formula for Company A, which charges 120 dollars upfront and 15 dollars per hour of labor.

Now, Company B charges 95 dollars upfront and 20 dollars per hour of labor. We can write the following equation:

The question asks us to find how many hours of labor that a repair must take in order for Company A to be cheaper than Company B. In other words, we need to compose an inequality in which the cost of Company A is less than the cost of Company B. We will substitute the variable  for hours and solve. 

Subtract  from each side of the inequality.

Subtract 95 from both sides of the inequality.

Divide both sides of the inequality by 5. 

If the repair will take more than 5 hours, Company A will be cheaper.