ACT Math - How to evaluate algebraic expressions

If , then which of the following is an expression for in terms of and ?

$\frac{F}{E}$

$\frac{E}{F}$

Explanation

Divide both sides by , giving you

$G=\frac{E}{F}$ .

A company establishes a rewards program such that the bonus received by an employee is given by the model $b = \frac{s^3}{10}$ , where is the number of sales an employee completed. If Alex earned $2700 at the end of the month, how many sales has he completed?

Explanation

Alex’s bonus of

$2700 = \frac{s^3}{10} \rightarrow 27000 = s^3\rightarrow s = 30.$

Evaluate the expression for

Explanation

The answer is

To solve this expression subsitute for . This results in . Simplify to get as the answer.

Sally is ordering snacks for her class trip. She needs 85 cookies. The cookies come in cases of 6 boxes, with 7 cookies in each box. Sally can't order a partial box. What is the smallest number of cases she should order?

Explanation

We first determine how many cookies are in each box. There are 7 cookies in a box, multiplied by 6 boxes, making 42 cookies in a case. We then divide the total number of cookies she needs, 85, by the number in each case, 42, giving us 2 with a remainder. This means Sally must order 3 cases of cookies.

If st – 4_r_ = 8, what is the value of t in terms of r and s?

(4r + 8)/s

(8 – 4r)/s

(4s + 8)/r

(8 – 4s)/r

s(4r + 8)

Explanation

We rearrange the equation st – 4r=8 by adding 4r to the right side; then divide by s → t = (4r + 8)/s

Which of the following is equal (10 – 6)2 if x = 10?

(x + 6)(x – 6)

(x + 4)(x – 4)

(x + 6)(x – 4)

(x – 8)(x – 2)

(x + 8)(x + 2)

Explanation

First, you set up and solve the original equation. Set up (10 – 6)2, then solve it, giving you 16. We can then plug in 10 for x in the answer choices until you find the choice that always gives you 16, which is (x – 8)(x – 2).

The expression x(9 + x)(x – 2) = 4 is a polynomial of which degree?