Chris, Casey, and Lisa worked together to build a mechanical unicorn. Casey worked twice as many hours as Chris. Lisa worked 10 more hours than Casey. Altogether, they worked 100 hours. How many hours did Lisa work?

Step 1: Assign Variables

Chris=

Casey =

Lisa=

Chris+ Casey + Lisa= 100.

𝑥2 𝑥2 𝑥+10

Step 2: Set up an equation showing that Chris, Casey, and Lisaworked 100 hours.

Chris+ Casey + Lisa= 100.

+ + 2 𝑥+10 Step 3: Combine Like Terms

5 𝑥+10=100 Step 4: Get variable by itself; subtract/divide

5 𝑥+10=100−10−105 𝑥¿905 5

𝑥=18

Chris = x

Casey = 2x

Lisa = 2x + 10

Step 5: Solve for Jeff

If x = 18, then:

18 hours

2(18) +10=46h𝑜𝑢𝑟𝑠

𝑳𝒊𝒔𝒂𝒘𝒐𝒓𝒌𝒆𝒅𝟒𝟔𝒉𝒐𝒖𝒓𝒔 .

¿100

PROBLEM 1: SUBSTITUTION (4 PTS)

𝑥2−2 𝑥−5

Evaluate. 𝑥=−7

(−7 )2−2(−7)−5

49−(−14 )−5 49+14−5

58

PROBLEM 2: SUBSTITUTION (4 PTS)

Evaluate. 𝑎=−2∧𝑏=−5

|𝑎2−𝑏2|2𝑎−𝑏

|(−2)2−(−5)2|2 (−2)−(−5)

|4−25|−4+5

|−21|1

211

21

PROBLEM 3: FORMULAS (4 PTS)A visitor to the Grand Canyon accidently dropped her sunglasses over the edge. It took 9 seconds for the sunglasses to fall directly to the bottom of the canyon. How far above the canyon bottom was she? [Hint: You may want to use d=rt or d=16t2.]

𝑑=16 𝑡2 𝑑=16(9)2 𝑑=16(81)

𝑑=1,296 𝑓𝑒𝑒𝑡

PROBLEM 4 (14 PTS)

1𝑥=¿¿ −1𝑤=¿¿

−2 (9 𝑦 )=¿¿ −(8 𝑥−9)=¿¿

3 (4 𝑥−5 𝑦+6)=¿¿

(−5𝑟 )(−7𝑏)(−2𝑥)=¿¿

a. b.

c. d.

e.

f.

𝒙 −𝒘

−𝟏𝟖𝒚 −𝟖 𝒙+𝟗

𝟏𝟐𝒙−𝟏𝟓𝒚+𝟏𝟖

−𝟕𝟎𝒃𝒓𝒙

Simplify.

PROBLEM 5 (6 PTS)

a. How many terms does the expression have? ____________ 3

b. What is the coefficient of ? ________-5

c. Combine like terms: __________________+ 7-2x

PROBLEM 6 (4 PTS)

Simplify:

6 𝑥+8−12𝑥−15

−𝟔 𝒙−𝟕

PROBLEM 7 (4 PTS)

Solve: +7 𝑎+7 𝑎

6 0 ¿9𝑎−3+3+3

63

¿

9𝑎9 97 𝑎

¿

PROBLEM 8 (4 PTS)

Solve:

6 𝑥−10¿62+10 +10

6 𝑥¿726 6

𝑥¿12

PROBLEM 9 (9 PTS)

Translate from English to algebra.

a. 8 less than the square of a number. ___________𝑥2−8

b. The quotient of 7 and twice a number. _______

72𝑛

c. The sum of 25 and 5 times a number. _______

25+5 y

PROBLEM 10 (4 PTS)

Twenty-five more than twice a number is the same as six times the number decreased by seven.

Variable Let 2x = twice the number, and let 6x = six times the number, and x= the number

Equation 25+2 𝑥=6 𝑥−7

PROBLEM 11 (4 PTS)

An editor needs to read a 680-page document. Her goal is to read 20 pages per day. If she has already read 260 pages, how many days will it take her to complete the proofreading?

Variable Let d= the number of days it will take her to complete the proofreading

Equation 680−26020

=𝑑 20𝑑=680−260OR

PROBLEM 12 (4 PTS)

The length of a rectangle is three times its width. If the perimeter is 328, find the length and the width of the rectangle.

Variable

Equation

h𝑤𝑖𝑑𝑡 =𝑥h𝑙𝑒𝑛𝑔𝑡 =3 𝑥

𝑥 𝑥

3 𝑥

3 𝑥

2 (3 𝑥+𝑥 )=3282 (3 𝑥 )+2(𝑥)=328

8 𝑥=328

OR

OR

PROBLEM 13 (3 PTS)Twenty-fives more than twice a number is the same as six times the number decreased by seven. Find the number.

Solve 25+2 𝑥=6 𝑥−7−2 𝑥−2 𝑥¿25 4 𝑥−7+7+7

32¿4 𝑥44

8¿𝑥

Check25+2 (8)=6(8)−7

41=41

?

State: The number is 8.

PROBLEM 13 (3 PTS)An editor needs to read a 680-page document. Her goal is to read 20 pages per day. If she has already read 260 pages, how many days will it take her to complete the proofreading?

Solve 680−26020

=𝑑 42020

=𝑑 21=𝑑

Check 680−26020

=21?

State: It will take her 21 days to finish proofreading.

PROBLEM 13 (3 PTS)The length of a rectangle is three times its width. If the perimeter is 328, find the length and the width of the rectangle.

Solve𝑥 𝑥

3 𝑥

3 𝑥

2 (3 𝑥+𝑥 )=3286 𝑥+2 𝑥¿3288 𝑥¿3288 8𝑥¿41

Check 8(41) = 328?

328 = 328State: The length is 123 units and the width is 41 units.

3 (41 )=123

Remember:Length= 3xWidth = x

PROBLEM 14

𝐶=5(𝐹−32)÷9

Use the formula to convert 86

𝐶=5(86−32)÷ 9

𝐶=5(54 )÷9

𝐶=270÷9𝐶=30 °

VOCABULARY (10PTS)1. The word quotient indicates the operation of _____________.division

2. To evaluate for we ____________ -3 for a and apply the rules for order of operations.substitute

3. A _____________ is an equation that states the relationship between two or more variables.

formula

VOCABULARY (10PTS)4. To _____________ an expression is to write it in simpler form.

simplify

5. To perform the multiplication 2(x+8), we use the ____________ property.distributive

6. A term that consists of a single number (and no variable) is called a _____________ term.

constant

VOCABULARY (10PTS)7. When we write 9x + x as 10x, we say we have ____________ like terms.combined

8. To _____________ an equation means to find all values of the variable that make the equation true.

solve

9. A number that makes an equation true is called a ____________.solution

10. A letter that is used to represent a mystery number is called a ____________.variable

VOCABULARY (10 PTS)