Solving Equations
Solving Inequalities
Rational/Irrational
Elimination/Substitution/Graphing
Translating Word Problems
100
Solve 
x = 20
100
4x + 1 − 1 ≥ −8
x ≥ -2
100
Which of the following is a rational number?
1. √8
2. π
3. 5√9
4. 6√2
3. 5√9 because 9 is a perfect square
100
When solved graphically, which system of equations will have exactly one point of intersection?
1) y = −x − 20 and y = x + 17
2) y = 0.5x + 30 and y = 0.5x − 30
3) y = 3/5 x + 12 and y = 0.6x − 19
4) y = −x + 15 and y = −x + 25
1) y = −x − 20 and y = x + 17
100
The cost of 3 markers and 2 pencils is $1.80. The cost of 4 markers and 6 pencils is $2.90. Write a system of equations that models this problem.
3m + 2p = 1.80
4m + 6p = 2.90
200
6x + 5 = 10 + 5x
x = 5
200
2p − 4p + 4 ≤ −2
p ≥ 3
200
The number 0.14114111411114 . . . is
1. Irrational
2. Rational
3. Whole
4. Integral
Irrational because it may not be expressed as the ratio of two integers. Nor is it a repeating decimal.
200
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of mushroom pizza?
$2.00 for a slice of mushroom pizza
200
The Celluloid Cinema sold 150 tickets to a movie. Some of these were child tickets and the rest were adult tickets. A child ticket cost $7.75 and an adult ticket cost $10.25. If the cinema sold $1470 worth of tickets, WRITE a system of equations could be used to determine how many adult tickets, a, and how many child tickets, c, were sold.
a + c = 150
10.25a + 7.75c = 1470
300
3(a + 22) = 12a + 30
a = 4
300
−2(b + 1) + 4 < 10
b > -4
300
The value of √x2 - 9 is a real and irrational number when x is equal to
1. 5
2. 0
3. -3
4. 4
4. 4
300
Using the substitution method, Vito is solving the following system of equations algebraically:
y + 3x = −4
2x − 3y = −21
Which equivalent equation could Vito use?
1) 2(−3x − 4) + 3x = −21
2) 2(3x − 4) + 3x = −21
3) 2x − 3(−3x − 4) = −21
4) 2x − 3(3x − 4) = −21
3) 2x − 3(−3x − 4) = −21
300
A high school drama club is putting on their annual theater production. There is a maximum of 800 tickets for the show. The costs of the tickets are $6 before the day of the show and $9 on the day of the show. To meet the expenses of the show, the club must sell at least $5,000 worth of tickets. Write a system of inequalities that models this problem.
x + y ≤ 800
6x + 9y ≥ 5000
400
2(-3y + 5) = -4(y + 4)
y = 13
400
20 − 2x > −2(x + 2) + 4x
x < 6
400
Given: √99/11, √164, and √196
Identify the expression that is a rational number and explain why it is rational.
√196 because it becomes 14, which is a whole number, meaning its rational.
400
Last week, a candle store received $355.60 for selling 20 candles. Small candles sell for $10.98 and large candles sell for $27.98. How many large candles did the store sell?
8 large candles sold
400
Cans of lemonade sell for $2 each and bottles of water sell for $1.50 each. The club needs to raise at least $500 to cover the cost of renting costumes. The students can accept a maximum of 360 cans and bottles. Write a system of inequalities that can be used to represent this situation.
2L + 1.5W ≥ 500
L + W ≤ 360
500
2(x - 3) = 1/2(4x - 12)
Infinite Solutions
500
2(1 − 4r) < −2(r + 3) − 4
r > 2
500
Ms. Fox asked her class "Is the sum of 4.2 and √2 rational or irrational?" Patrick answered that the sum would be irrational. State whether Patrick is correct or incorrect. Justify your reasoning.
Patrick is correct as the number you get cannot be simplified as a fraction. A rational plus an irrational will always be an irrational.
500
What is the solution of the following system of equations?
2a + 3b = 12
a = (1/2)b − 6
1) a = −6 and b = 0
2) a = −4.5 and b = 3
3) a = −3 and b = 6
4) a = 24 and b = 6
3) a = −3 and b = 6
500
Football player McGee’s earnings, m, were 0.005 million dollars more than those of his teammate Fitzpatrick’s earnings, f. The two players earned a total of 3.95 million dollars. Which system of equations could be used to determine the amount each player earned, in millions of dollars?
1. m + f = 3.95 and m + 0.005 = f
2. m - 3.95 = f and f + 0.005 = m
3. f - 3.95 = m and m + 0.005 = f
4. m + f = 3.95 and f + 0.005 = m
1. m + f = 3.95 and m + 0.005 = f