ACT Math : Algebra
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Example Question #23 : How To Find The Solution To An Equation
Sally sells hair accessories. Her monthly fixed costs are $150. It costs her $5 to make each barrette, and she sells them for $10 each.
If Sally wants to make a profit of $250, how many barrettes must she sell?
Let 
Revenue will be equal to 
Costs will be equal to 
The equation to solve becomes 
To reach the profit goal of $250, we need to calculate the value of 
Example Question #301 : Algebra
What are the values for x that satisfy the equation (x-d)(x+c)=0?
dc
-dc
d and c
d and -c
–d and c
d and -c
Set each component of this equation equal to zero and solve for d and c.
(x-d)(x+c)=0
x-d=0
d=0
x+c=0
x=-c
Example Question #302 : Algebra
If A + B = C and B – C = 3, what does A equal?
6
–9
–3
3
9
–3
This question can be solved using substitution. There are several ways to subsitute, but one possible method is to substitue (A+B) for C in the equation B-C=3: B-(A+B)=3. This simplifies to (B-A-B=3) (don't forget to distribute the negative!). Since (B-B)=0, -A must equal 3 (-A=3). If we divide both sides by -1, A=-3. If you got an answer of positive 3, you may have forgotten to divide both sides by -1.
Example Question #303 : Algebra
The population of a bird species is modeled by the following equation:
where 
280.8
20.4
12.2
23.0
38.5
20.4
Plugging in 130 for P, the equation becomes 130 = (11/8)x + 102. Solving for x, we obtain x = 20.4 years.
Example Question #304 : Algebra
What is the value of c when 3c + 4 = 2c – 7?
1
0
No Solution
11
–11
–11
First put the variables on one side by subtracting 2c on both sides to get c + 4 = –7. Then subtract the 4 on both sides to arrive at your answer, c = –11.
Example Question #305 : Algebra
If y=0.35(300 – 2y), what is the value of y to the nearest tenth?
61.8
65.0
62.3
51.2
61.8
Distributing the 0.35 to both the 300 and –2y leaves y=105 – 0.7y
Adding 0.7y to both sides and dividing by 1.7 gives 61.8.
Example Question #29 : How To Find The Solution To An Equation
Which of the lines below is not parallel to 4x – 3y = 17 ?
–y= –(4/3)x – (17/3)
8x – 6y = 34
2x – 1.5y = 8.5
8x + 6y = 34
8x + 6y = 34
For a line to be parallel with another, the slopes must be equal. All of the equations have a slope of 4/3 except 8x +6y=34.
Example Question #30 : How To Find The Solution To An Equation
If the expression x4 + 3cx – 2 is equal to 5 when x = –1, what is the value of c?
3
2
–2
1
–2
Plugging in –1 into the equation for x and solving for c yields –2.
Example Question #306 : Algebra
What is the slope of the line 7y – 4x = 27
Adding 4x to both sides of the equation and dividing by 7 yields a slope of 4/7.
Example Question #32 : How To Find The Solution To An Equation
If you drove at an average speed of 78 miles per hour, what distance, in miles, did you drive in 140 minutes?
182
4,680
156
1.8
182
140 minutes is 7/3 of an hour. Multiplied by the speed of 78mph, we obtain 182 miles traveled.
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