Wherever there is an x, plug in 11 and perform the given operations. The numerator will be equal to 83 and the denominator will be equal to 46. 83 divided by 46 is equal to 1.804… and since the second decimal place is not greater than or equal to 5, the first decimal place stays the same when rounding so the final answer is 1.8.

To begin a problem like this, you must first convert everything to  and  alone. This way, you can begin to cancel and combine to its most simplified form.

Since  and , we insert those identities into the equation as follows.

From here we combine the numerator and denominators of each fraction together to easily see what we can combine and cancel.

Since there is a  in the numerator and the denominator, we can cancel them as they divide to equal 1. All we have left is , the answer. 

Solve for the variables, the plug into formula.

x = 12/3 = 4

y = 10 * 4 = 40

z= 9/4 = 2 ¹/₄

10xyz = 3600

Xy = 160

3600/160 = 22 ¹/2

In order to solve , we must first find the values of , , and  using the initial equations provided. Starting with :

Then:

Finally:

With the values of , , and  in hand, we can solve the final equation:

In order to solve , first substitute the values of  and  provided in the problem:

Find the Least Common Multiple (LCM) of the fractional terms in the denominator and find the equivalent fractions with the same common denominator:

Finally, in order to divide by a fraction, we must multiply by the reciprocal of the fraction:

In order to solve for , first substitute  into the equation for :

Then, find the Least Common Multiple (LCM) of the two fractions and generate equivalent fractions with the same denominator:

Finally, simplify the equation:

Factor out 7 from the numerator:

This simplifies to 7.

If 10 pizzas cost x dollars, then each pizza costs x/10. Similarly, each soda costs y/6. We can add the pizzas and sodas together by finding a common denominator:

Since the values in the pie charts are currently in terms of percentages (/100), we must convert them to degrees (/360, since within a circle) to solve the question. The "5 to 9 years" portion for the financial and construction industries are 18 and 25 percent, respectively. As such, we can cross-multiply both:

18/100 = x/360 

x = 65 degrees

25/100 = y/360

y = 90 degrees

Subtract: 90 – 65 = 25 degrees

Alternatively, we could first subtract the percentages (25 – 18 = 7), then convert the 7% to degree form via the same method of cross-multiplication.

When there are 6 people playing, each contestant has a 1/6 chance of winning.  After the disqualification, the remaining contestants have a 1/5 chance of winning.

1/5 – 1/6 = 6/30 – 5/30 = 1/30.