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ACT Math : Algebra

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Example Questions

Example Question #311 : Algebra

3x + 9i² – 5x = 17

What is x?

Possible Answers:

–1

–13

–4

Correct answer:

–13

Explanation:

i = $\sqrt{-1}$

i²= -1

3x + 9i² – 5x = 17

3x + 9(–1) – 5x = 17

–2x – 9 = 17

–2x = 26

x = –13

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Example Question #312 : Algebra

Solve for x:

3x + 4y = 26

–5x + 12y = 14

Possible Answers:

$\frac{46}{7}$

$\frac{32}{7}$

$-\frac{7}{32}$

$-\frac{32}{7}$

$\frac{7}{32}$

Correct answer:

$\frac{32}{7}$

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

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Example Question #313 : Algebra

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 $V_{1}N_{1} + V_{2}N_{2} + V_{3}N_{3} =$ $\$\ total$ , where is the value of the coin and is the number of coins.

Let = # of dimes, x + 1 = # of quarters, and x - 1 = # of nickels.

So, 0.10x + 0.25(x + 1) + 0.05(x - 1) = 2.60 , and solving gives x = 6 . Therefore there are 6 dimes, 7 quarters, and 5 nickels, giving 18 coins in total.

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Example Question #1804 : Act Math

What value of will satisfy the equation

5(z+3)= 2z+12

Possible Answers:

3/7

-3/7

Correct answer:

Explanation:

The answer is .

The solve this equation, first distribute the to obtain 5z+15= 2z+12

Proceed to subtract from both sides to get 3z+15=12

Subtract from both sides to leave 3z=-3

Divide both sides by to get the answer, z=-1

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Example Question #34 : Equations / Inequalities

Given that 2x+1=3x-2 , what is the value of ?

Possible Answers:

$\frac{5}{7}$

$\frac{3}{2}$

Correct answer:

Explanation:

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

2x-2x+1=3x-2x-2

1=x-2

Then we must add to both sides:

1+2=x-2+2

3=x

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Example Question #35 : How To Find The Solution To An Equation

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:

5.00 + 0.20 (x)

5.00 + 0.20 (x-10)

5.00

10 + 0.20 (x-10)

5 + 0.20 (x+10)

Correct answer:

5.00 + 0.20 (x-10)

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

$\$0.20(x-10)+5$ .

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

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

Possible Answers:

b-c

c/b

c-b

b/c

c+b

Correct answer:

b/c

Explanation:

If we take the units and look at division, miles/(miles/hour) will yield hours as a unit. Therefore the answer is b/c .

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Example Question #33 : How To Find The Solution To An Equation

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:

$125\ mph$

$275\ mph$

$225\ mph$

$175\ mph$

$300\ mph$

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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Example Question #34 : How To Find The Solution To An Equation

How much water should be added to $2\ L$ of 90% cleaning solution to yield 50% cleaning solution?

Possible Answers:

$1.5\ L$

$0.8\ L$

$1.6\ L$

$1.2\ L$

$2.4\ L$

Correct answer:

$1.6\ L$

Explanation:

Pure water is 0% and pure solution 100%. Let $x$ = water to be added.

$V_{1}P_{1} + V_{2}P_{2} = V_{f}P_{f}$ in general where $V$ is the volume and $P$ is the percent.

So the equation to solve becomes $x(0)+2(0.90)= (x+2)(0.50)$

and $x=1.6\ L$

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Example Question #35 : How To Find The Solution To An Equation

Solve $x+2y=14$ and $2x+y=13$

Possible Answers:

$(1,3)$

$(4,5)$

$(3,2)$

$(-4,-5)$

$(5,4)$

Correct answer:

$(4,5)$

Explanation:

This problem is a good example of the substitution method of solving a system of equations. We start by rewritting the first equation in terms of $x$ to get $x=14-2y$ and then substutite the $x$ into the second equation to get

$2(14-2y)+y=13$ .

Solving this equation gives $y=5$ and substituting this value into one of the original equations gives $x=4$ , thus the correct answer is $(4,5)$ .

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ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #311 : Algebra

Example Question #312 : Algebra

Example Question #313 : Algebra

Example Question #1804 : Act Math

Example Question #34 : Equations / Inequalities

Example Question #35 : How To Find The Solution To An Equation

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

Example Question #33 : How To Find The Solution To An Equation

Example Question #34 : How To Find The Solution To An Equation

Example Question #35 : How To Find The Solution To An Equation

All ACT Math Resources

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