The total volume is 5 * 5 * 4 = 100 cm³ . Half of this is 50 cm³ which is 50 mL.

This is a rate problem. We need to first find out how many treats a day the dog eats. Then to find the number of treats the dog eats in \(\displaystyle 4+x\) days, we multiply the number of days by the number of treats a day the dog eats.

From the given information, we know that the dog eats \(\displaystyle \frac {9}{4}\) treats a day.

Then we multiply that number by the number of days.

\(\displaystyle \frac{9}{4}(4+x)\)

Now simplify.

\(\displaystyle 9+\frac{9x}{4}\)

The total drink is made up of \(\displaystyle 3+4+3=10\:oz\). Therefore, for a problem like this, you can set up a ratio:

\(\displaystyle \frac{x}{10}=\frac{237}{3}\)

First, simplify the right side of the equation:

\(\displaystyle \frac{x}{10}=79\)

Next, solve for \(\displaystyle x\):

\(\displaystyle x=790\).  Therefore, the total amount of drink is \(\displaystyle 790\:oz\).

To begin with, you need to compute what is going to be your limiting factor. For the cream, you can make:

\(\displaystyle \frac{350}{2.5}=140\) servings.

For the coffee, you can make:

\(\displaystyle \frac{450}{4}=112.5\) servings. 

Therefore, this second value is your total number of servings. (You must choose the minimum, for it will be what limits your beverage-making.)

So, you know that each drink is \(\displaystyle 4+3+2.5+1=10.5\:oz\).  If you can make \(\displaystyle 112\) servings (remember, no partial servings!), you can make a total of \(\displaystyle 112*10.5=1176\:oz\).

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

\(\displaystyle \frac{4}{7}=\frac{x}{161}\), where \(\displaystyle x\) is the number of cups of orange juice.

Now, solving for \(\displaystyle x\), you get:

\(\displaystyle x=92\)

Be careful, though! This means that the total solution is actually \(\displaystyle 92+161\) or \(\displaystyle 253\).

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

\(\displaystyle \frac{3}{5}\)

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:

\(\displaystyle \frac{3}{5}=\frac{x}{240}\)

Solving for X, you get:

\(\displaystyle x=144\)

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:

\(\displaystyle 144 + 240\) or \(\displaystyle 384\textup{ml}\)

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 \(\displaystyle 1:3\).

Without simplifying, the ratio of green to blue is \(\displaystyle 3:9\) (order does matter).

Since 3 and 9 are both divisible by 3, this ratio can be simplified to \(\displaystyle 1:3\).

Let \(\displaystyle 10x\) be the number of store employees, \(\displaystyle 3x\) the number of store managers, and \(\displaystyle x\) the number of corporate managers.

\(\displaystyle 10x+3x+x=126\)

\(\displaystyle 14x=126\)

\(\displaystyle x=9\)

\(\displaystyle 10x=10\times9=90\), so the number of store employees is \(\displaystyle 90\).

\(\displaystyle 3x=3\times9=27\), so the number of store managers is \(\displaystyle 27\).

\(\displaystyle x=9\), so the number of corporate managers is \(\displaystyle 9\).

Therefore, the number of employees who are either store managers or corporate managers is \(\displaystyle 27+9=36\).