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High School Math : Equations

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Example Question #31 : Equations

is what percent of ?

Possible Answers:

Correct answer:

Explanation:

Verbal cues include "IS" means equals and "OF" means multiplication.

So the equation to solve becomes

$15=P\cdot 75$ and dividing both sides by gives $P=0.20 \; or \; 20\%$

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Example Question #1 : Systems Of Equations

Solve the system of equations.

4x+y=16

2x+3y=18

Possible Answers:

(-3,4)

(4,3)

(3,4)

(-4,3)

None of the other answers are correct.

Correct answer:

(3,4)

Explanation:

Isolate in the first equation.

y=16-4x

Plug into the second equation to solve for .

2x+3(16-4x)=18

2x+48-12x=18

-10x+48=30

-10x=-30

x=3

Plug into the first equation to solve for .

4(3)+y=16

12+y=16

y=4

Now we have both the and values and can express them as a point: (3,4) .

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Example Question #1 : Solving Equations

Solve for and .

3x+2y=2

2x+2y=4

Possible Answers:

$x=-2\ and\ y=8$

$x=-2\ and\ y=4$

$x=2\ and\ y=-8$

Cannot be determined.

$x=2\ and\ y=-4$

Correct answer:

$x=-2\ and\ y=4$

Explanation:

1st equation: 3x+2y=2

2nd equation: 2x+2y=4

Subtract the 2nd equation from the 1st equation to eliminate the "2y" from both equations and get an answer for x:

Plug the value of into either equation and solve for :

2(-2)+2y=4

-4+2y=4

2y=4+4

2y=8

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Example Question #31 : Equations

Solve for :

$\left | 5x + 39 \right | = 44$

Possible Answers:

$x = -16\frac{3}{5} \textrm{ or } x = 1$

$x = 16\frac{3}{5}$

$x = -1 \textrm{ or } x = 1$

$x = 1 \textrm{ or }x = 16\frac{3}{5}$

$x = -16\frac{3}{5} \textrm{ or }x = 16\frac{3}{5}$

Correct answer:

$x = -16\frac{3}{5} \textrm{ or } x = 1$

Explanation:

Rewrite $\left | 5x + 39 \right | = 44$ as a compound statement and solve each part separately:

$\left | 5x + 39 \right | = 44$

$5x + 39 = - 44 \textrm{ or }5x + 39 = 44$

5x + 39 = - 44

5x + 39 - 39 = - 44- 39

5x = - 83

$5x \div 5 = - 83 \div 5$

$x = -16\frac{3}{5}$

5x + 39 = 44

5x + 39 - 39 = 44- 39

5x = 5

$5x \div 5 =5 \div 5$

x = 1

Therefore the solution set is $\left \{-16\frac{3}{5}, 1 \right \}$ .

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Example Question #33 : Equations

Solve the following equation for :

3(x+2) = 4(x-3)

Possible Answers:

x = 2

x = 18

x = -18

x = -9

x = -6

Correct answer:

x = 18

Explanation:

3(x+2) = 4(x-3)

The first step in solving this equation is to distribute the 3 and the 4 through the parentheses:

$3\cdot x+3\cdot2 = 4\cdot x-4\cdot 3$

Simplify:

3x+6 = 4x-12

Now, we want to get like terms on the same sides of the equation. That is, all of the terms with an should be on one side, and those without an should be on the other. To do this, we first subtract from both sides:

3x+6 -4x= 4x-12-4x

Simplify:

-x+6 = -12

Now, we subtract 6 from both sides:

-x+6-6 = -12-6

-x = -18

x = 18

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Example Question #34 : Equations

Goldenrod paint is made by mixing one part red with three parts yellow. How many gallons of yellow paint should be mixed with two quarts of red paint?

Possible Answers:

$0.75\; gallons$

$1.50\; gallons$

$1.00\; gallon$

$1.25\; gallons$

$1.75\; gallons$

Correct answer:

$1.50\; gallons$

Explanation:

This problem is solved using proportions and the following conversion factor:

$4\; quarts=1\; gallon$

Let yellow quarts of paint.

$\frac{red}{yellow}=\frac{1}{3}=\frac{2\; quarts}{x\; quarts}$

Then cross multiply to get $x=6\; quarts = 1.50 \; gallons$ .

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Example Question #35 : Equations

Solve for :

$\frac{1}{2}(x+3)=\frac{1}{3}(x+5)$

Possible Answers:

Correct answer:

Explanation:

Multiply both sides by to eliminate the fractions to get 3(x+3)=2(x+5) .

Then use the distributive property to get 3x+9=2x+10 .

Now subtract from both sides to get x+9=10 .

Now subtract from both sides to get x=1 .

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Example Question #36 : Equations

To mail a package, there is an initial charge of $55\cent$ to cover the first ounce, with another $25\cent$ for each additional ounce. How much does it cost to mail a half pound package?

Possible Answers:

$\$ 3.50$

$\$ 2.30$

$\$ 3.95$

$\$ 4.40$

$\$ 2.00$

Correct answer:

$\$ 2.30$

Explanation:

$1\; pound = 16 \; ounces$ , so we are trying to mail ounces. The total postage becomes $0.55+7(0.25)=0.55+1.75=\$ 2.30$ .

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High School Math : Equations

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #31 : Equations

Example Question #1 : Systems Of Equations

Example Question #1 : Solving Equations

Example Question #31 : Equations

Example Question #33 : Equations

Example Question #34 : Equations

Example Question #35 : Equations

Example Question #36 : Equations

All High School Math Resources

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