Unit 3 - Intro to Algebra

Simplifying Pt 1

100

3p x 4p

12p^2

200

2r(4r)^2

32r^3

300

8ytimes3ydivide2x

(12y^2)/x

400

(3a)^2b^2+(4b)^2a^2

25a^2b^2

500

-4(2x - 3y) - 2(5x + y)

-18x+10y

Simplifying Pt 2

100

4mn-10mn

-6mn

200

3(m - 5) + m

4m - 15

300

(5b)^2-3ctimes2d

25b^2-6cd

400

2(5a + 10) - 3(2a + 1) + 4(a + 5)

8a + 37

500

5x - 2[ 3(x - 2) + 4 ]

-x+4

Real World

100

Paul is 4 inches taller than Bree

Given that Paul's height is “p” feet, write a formula connecting “b” and “p”

p=1/3+b 

200

Brad planted some flowers. Alison planted 5 fewer than three times the number of flowers Brad planted. Carly planted double the number of flowers Alison planted. Let a, b, and c be the number of flowers planted by Alison, Brad, and Carly.

• a) Express a and c in terms of b.
• b) If Brad planted 8 flowers, how many flowers did Alison and Carly plant?

Part a:

• a = 3b - 5
• c = 6b - 10

Part b:
If b = 8:

• a = 3(8) - 5 = 24 - 5 = 19
• c = 6(8) - 10 = 48 - 10 = 38 

300

Benny scored a certain number of points. Alice scored 40 points less than twice Benny's score. Christy scored 100 points more than Alice's score. Let a, b, and c be the scores of Alice, Benny, and Christy.

a) Express a and c in terms of b.

b) If Benny scored 150 points, what are the scores of Alice and Christy?

Part a:

a = 2b-40

c = 2b+60

Part b

a = 2(150) - 40 = 260

c = 2(150)+60 = 360

400

David’s weekly running distance is 8 miles less than twice Emily’s weekly distance. Frank’s weekly running distance is 3 miles more than three-fourths of David’s weekly distance. Let d, e, and f be the weekly distances (in miles) of David, Emily, and Frank.

• a) Express d and f in terms of e.
• b) If Emily runs 12 miles in a week, how many miles do David and Frank run?

Part a

d = 2e - 8

f = 1.5e - 3

Part b:
If e = 12:

d = 2(12) - 8 = 16

f = 1.5(12) - 3 = 18 - 3 = 15

500

The battery life of Smartphone A is 10 hours less than three times that of Smartphone B. The battery life of Smartphone C is 2.5 hours more than two-thirds of Smartphone A's battery life. Let a, b, and c represent the battery life (in hours) of Smartphones A, B, and C respectively.

• a) Express \(a\) and \(c\) in terms of \(b\).
• b) If Smartphone B has a battery life of 15 hours, what is the battery life of Smartphones A and C?

Part a:

a = 3b - 10

 c=2/3 a+2.5rightarrowc=2/3(3b-10)rightarrowc=2b-6.67+2.5rightarrowc=2b-4.17 

Part b:

a = 3(15) - 10 = 35

c = 2(15) - 4.17 = 25.83

• 
  

• \(a = 3(15) - 10 = \mathbf{35\text{ hours}}\)

• 
  

  
  

• \(c = 2(15) - 4.17 = \mathbf{25.83\text{ hours}}\)

• 
  

Evaluating Expressions

100

When x=3 and y=5

8y+2x

46

200

When x=4 and y=10

 (4x)/y^2 

4/25

300

When x=2 and y=5

 2y^3-(2x)^3 

234

400

 When x=3 and y=5

(x^2+y^2)/(x-y)^3 

-4 1/4 or -4.25

500

Evaluate  4 - [x - (y^2 - 2z)]  when x = -1, y = -2, and z = -5

19

Evaluating Formulas

100

A = 1/2bh

when b=13 and h=23

149.5

200

 F=9/5(C+32) 

Solve for F when C = -12

36

300

 A=pir^2 

Find A when pi = 3.14 and r = 8

25.12

400

  S = h(a + b) + L(a + b + c + d) 
Find S when h = 4.5, a = 6, b = 10, c = 5, d = 5, and L = 12.5

397

500

Formula:  A = P(1 + \frac{r}{n}\)^{nt}  

Find A when P = 25, r = 8, n = 4, and t = 1/2

225