# ACT Math : Variables

## Example Questions

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### Example Question #1 : Variables

Mike wants to sell candy bars for a  profit. If he sells each bar for , how much did each bar cost him?

Explanation:

In order to solve this problem, set up the following equation:

Cross multiply:

Divide:

The original cost of the of each candy bar is

### Example Question #2 : Monomials

Choose the answer that is the simplest form of the following expression of monomial quotients:

Explanation:

To divide monomial quotients, simply invert the divisor and multiply:

Then, reduce:

### Example Question #1 : Variables

Choose the answer that is the simplest form of the following expression of monomial quotients:

Explanation:

To find your answer, you have to invert the divisor and multiply across:

Then, reduce:

### Example Question #1 : Monomials

Multiply:

Explanation:

To solve you must multiply  by both terms in

### Example Question #5 : Monomials

Multiply:

Explanation:

Multiply  by both terms in

### Example Question #6 : Monomials

Multiply

Explanation:

When multiplying a polynomial by a monomial, each term in the polynomial gets multiplied by the monomial. Calculate each term one at a time, then add the results to get the final answer. In this case, we start by multiplying  and , thus we get . For the second term of the polynomial, we multiply  and , resulting in . Finally, we multiply  and , resulting in . Adding the three terms that we just found, we come to the answer of .

### Example Question #1 : Variables

Choose the answer that is the best solution to the following expression of monomial quotients:

Explanation:

To multiply monomial quotients, treat them as you would any other fraction. Combine like terms wherever possible:

Then, you need to reduce:

### Example Question #1 : Variables

Choose the answer that is the simplest form of the following expression of monomial quotients:

Explanation:

To simplify, first multiply across:

Then, reduce:

### Example Question #1 : Direct And Inverse Variation

The price of silver varies directly as the square of the mass. If 3.6 g of silver is worth $64.80, what is the value of 7.5 g of silver? Possible Answers:$178.50

$301.75$281.25

$135.00$215.25

$281.25 Explanation: This is a direct variation problem of the form y = kx2 The first set of data 3.6 g and$64.80 is used to calculate the proportionality constant, k.  So 64.80 = k(3.6)2 and solving the equation gives k = 5.

Now we move to the new data, 7.5 g and we get y = 5(7.5)2 to yield an answer of $218.25.$135.00 is the answer obtained if using proportions.  This is an error because it does not take into consideration the squared elements of the problem.

### Example Question #1 : Variables

The diameter of a specific brand of candy wrapper is  longer than half the volume of the candy itself. Find the expression for the diameter, , in terms of the volume, .