ACT Math : Equations / Inequalities

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #31 : Linear / Rational / Variable Equations

What is the slope of the line 7y – 4x = 27

Possible Answers:

Correct answer:

Explanation:

Adding 4x to both sides of the equation and dividing by 7 yields a slope of 4/7.

Example Question #31 : Linear / Rational / Variable Equations

If you drove at an average speed of 78 miles per hour, what distance, in miles, did you drive in 140 minutes? 

Possible Answers:

156

4,680

1.8

182

Correct answer:

182

Explanation:

140 minutes is 7/3 of an hour. Multiplied by the speed of 78mph, we obtain 182 miles traveled.

Example Question #32 : Linear / Rational / Variable Equations

3x + 9i2 – 5x = 17

What is x?

Possible Answers:

–4

–13

4

–1

13

Correct answer:

–13

Explanation:

i =

i2 = -1

3x + 9i2 – 5x = 17

3x + 9(–1) – 5x = 17

–2x – 9 = 17

–2x = 26

x = –13

Example Question #1801 : Act Math

Solve for x:

3x + 4y = 26

–5x + 12y = 14

Possible Answers:

Correct answer:

Explanation:

Eliminate y and solve for x.

3x + 4y = 26 (multiply by –3)

 

–5x + 12y = 14

(–3)3x +(–3) 4y = (–3)26

 

–5x + 12y = 14

–9x +-12y = –78

 

–5x + 12y = 14

–14x + 0y = –64

 

x = –64/–14 = 32/7

Example Question #32 : Linear / Rational / Variable Equations

Michael is counting his money.  He notices he has one more quarter than he does dimes, as well as one less nickel than dimes.  The total cash he has is $2.60.  How many coins does he have in total?

Possible Answers:

Correct answer:

Explanation:

The general form for money problems is V_{1}N_{1} + V_{2}N_{2} + V_{3}N_{3} = ,  where  is the value of the coin and  is the number of coins.

Let  = # of dimes,  = # of quarters, and  = # of nickels.

So, , and solving gives . Therefore there are 6 dimes, 7 quarters, and 5 nickels, giving 18 coins in total.

Example Question #31 : How To Find The Solution To An Equation

What value of  will satisfy the equation

Possible Answers:

Correct answer:

Explanation:

The answer is

The solve this equation, first distribute the  to obtain  

Proceed to subtract  from both sides to get

Subtract  from both sides to leave

Divide both sides by to get the answer,

Example Question #31 : How To Find The Solution To An Equation

Given that , what is the value of  ?

Possible Answers:

Correct answer:

Explanation:

First, we must solve the equation for  by subtracting  from both sides:

Then we must add  to both sides:

Example Question #121 : Equations / Inequalities

Internet service costs $0.50 per minute for the first ten minutes and is $0.20 a minute thereafter. What is the equation that represents the cost of internet in dollars when time is greater than 10 minutes?

Possible Answers:

Correct answer:

Explanation:

The first ten minutes will cost $5. From there we need to apply a $0.20 per-minute charge for every minute after ten. This gives

.

Example Question #134 : Algebra

John goes on a trip of  kilometers at a speed of  kilometers an hour. How long did the trip take?

Possible Answers:

Correct answer:

Explanation:

If we take the units and look at division,  will yield hours as a unit. Therefore the answer is .

Example Question #135 : Algebra

With a 25\ mph head wind a plane can fly a certain distance in five hours.  The return flight takes an hour less.  How fast was the plane flying?

Possible Answers:

125\ mph

300\ mph

175\ mph

275\ mph

225\ mph

Correct answer:

225\ mph

Explanation:

In general, distance=rate\times time

The distance is the same going and coming; however, the head wind affects the rate.  The equation thus becomes (r-25)\times 5=(r+25)\times 4.

Solving for r gives r=225\ mph.

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