Expressions, Equations, and Inequalities
Simplify the expression:
-9w -4x + 3(-5x +2w)
Answer: -3w - 19x or -19x - 3w
-9w -4x - 15x + 6w
-9w + 6w - 4x - 15x
-3w - 19x
Which of the following does not always show proportionality?
A) The ratio of the dependent variable to the independent variable is always the same.
B) The values of both variables increase by a constant amount.
C) The relationship can be graphed as a straight line through the origin.
D) The relationship can be represented as an equation of the form y=kx.
B) The values of both variables increase by a constant amount.
Ms. Hwang pays $1.88 in sales tax. Her subtotal is $27.09. What is the sales tax rate, rounded to the nearest tenth of a percent?
Answer: 6.9%
part = % x whole
sales tax = sales tax rate x subtotal
$1.88 = ? x $27.09
? = .0693983...
? x 100 = 6.93...
round to the nearest tenth 6.9%
10 students were randomly picked for their heights to be measured. The following data are their heights in inches:
62, 59, 57, 64, 68, 65, 60, 54, 56, 57
Find the five-number summary (minimum, q1, median, q3, maximum)
Answer: Minimum: 54, Q1: 57, Median: 59.5, Q3: 64, Maximum: 68
1) Re-order data
54, 56, 57, 57, 59, 60, 62, 64, 65, 68
2)Minimum = 54
Q1 (middle value of lower half)=57
Median =(59+60)/2 = 59.5
Q3 (middle value of upper half)= 64
Maximum = 68
How many solutions does the equation below have?
3 - 2x - 6 = 6 - (3 - 2x)
A) No Solutions
B) One Solution
C) Infinite Solutions
Answer: B) one solution
-3 - 2x = 6 -3 +2x
-3 - 2x = 3 + 2x (different coefficients and constants)
-3 - 2x = 3 + 2x
-6 - 2x = 2x
-6 = 4x
-6/4 = x or -3/2 = x
If 12 pencils cost 42 cents, how much would 100 pencils cost?
Answer: $3.50 or 350 cents
Cost per pencil = $0.42/12 = 3.5 cents per pencil
100 pencils x 3.5 cents per pencil = $3.50
A bicycle is on sale for $189.50. The sales tax rate is 5%. What is the total price?
Answer: $198.98
Tax = 189.50 x .05 = 9.475
Total = 189.50 + 9.475 = 198.975
Rounded to nearest cent is $198.98
A bag has 40 marbles.
40% of the marbles are red.
1/2 of the marbles are blue.
The remaining marbles are yellow.
How many yellow marbles are in the bag?
Answer: 4 yellow marbles
Red marbles = .40 x 40= 16
Blue Marbles = .50 x 40 = 20
Red + Blue = 16 + 20 = 36
40 total marbles - 36 red and blue = 4 yellow marbles
Solve the equation for x.
-3(x + 2.5) = 7.2x - 3 - 1.2x
Answer: -1/2 or -.5
-3x - 7.5 = 6x - 3
-9x - 7.5 = -3
-9x = 4.5
x = -1/2
Lisa paints a room that has 400 square feet of wall space in 2.5 hours. At this rate, how long will it take her to paint a room that has 720 square feet of wall space?
Answer: 4.5 hours
400 sq. feet/2.5 hours = 160 square feet per hour
Time = 720/160 = 4.5 hours
Ms. Lansing buys jeans for $36. She has a 12% off coupon and a $2 off coupon. She applies the 12% off coupon first and then the $2 off coupon. What is the total amount of money Ms. Lansing saved?
Answer: Ms. Lansing saved $6.32.
? = .12 x 36
? = 4.32
4.32 + 2 = $6.32
You play a game where you spin a spinner labelled 1-4 and flip a fair coin. What is the probability that you land on a number greater than 2 and land on heads?
Answer: 25% or 1/4 or .25
Favorable outcomes: 3H and 4H
Total Outcomes: 8
2/8 = 1/4
or multiply the probabilities of each event
P(number greater than 2) = 2/4 = 1/2
P(land on heads) = 1/2
1/2 x 1/2 = 1/4
Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 in the account by the end of the summer. He withdraws $25 each week for food, clothes, and movie tickets.
Inequality: 500 - 25w >= $200 (greater than or equal to)
500 - 25w >= 200
-25w >= -200
w <= 12
(He can withdraw money for at most 12 weeks)
A copying machine can reduce the size of the material being copied. A diagram measuring 16 cm wide by 20 cm long is reduced. If the diagram on the reduced copy is 15 cm long, what is its width?
Answer: The width of the reduced diagram is 12cm.
scale factor = new/original
scale factor = 15/20
scale factor = 0.75
16 cm x 0.75 = 12 cm
The Rodriguez family went to dinner at Pasta Palace. - - The dad ordered a meal for $6.25
- The mom ordered a meal for $7.50
- the 2 children ordered individual pizzas for $4.99 each
- The sales tax rate was 7.25% and they left a 15% tip. How much was the total bill?
Answer: $29.01
Subtotal: 6.25 + 7.50 + 9.98 (2 pizzas) = $23.73
Tax (percent of subtotal): 23.73 x .0725 = 1.720425
Tip (percent of subtotal): 23.73 x .15 = 3.5595
Total: 23.73 + 1.720425 + 3.5595 = 29.009925 rounds to $29.01
32 students filled out a survey about their favorite subject. 18 students chose ELA, 8 students chose Math, and the rest chose science.
Based on the results, how many students out of 430 will most likely pick science as their favorite subject?
Answer: Approximately 81 students will pick science as their favorite subject
32 - (18 + 8) = 6
6/32 = .1875 (18.75% picked science)
.1875 x 430 = 80.625
Round up to 81 students
A car rental agency charges $35 per day plus $0.10 per mile. If you have a budget of $100 and need the car for 2 days, what is the maximum number of miles you can drive?
Answer: You can drive at most 300 miles.
Inequality 2(35) + 0.10m < = 100
or 70 + 0.10m <= 100
Solve for m
0.10m <= 30
m <= 300
A doctor sees each of her patients for 25 minutes during a typical appointment. How many patients can she see in a typical 7.5 hour day?
Answer: 18 patients
7.5 hours = 7(60 minutes) + 30 minutes
7.5 hours = 420 + 30
7.5 hours = 450 minutes
25 minutes per patient or k=1/25
450 minutes x (1/25) = 18 patients
You buy a gallon of milk that costs $3.50. The milk is discounted for 11% off. You also have to pay tax of 6.25% on the discounted price. What is the final cost?
Answer: $3.31
Discount: ? = .11 x $3.50
? = .385
$3.50 - $0.385 = $3.115
Tax: ? = 6.25% of $3.115
? = .0625 x 3.115
? = .1946875
Total: 3.115 + .1946875 = 3.3096875
rounds to $3.31
There are two carnival games.
Game 1: Pick a marble out of a bag containing 7 orange marbles, 2 yellow marbles, and 1 blue marble. You win if you pick a yellow or blue marble.
Game 2: Flip a fair coin and spin a spinner labelled 1-4. You win if you get tails and an odd number.
Which game are you more likely to win?
Answer: You are more likely to win game 1 by 5% because P(winning game 1)= 30% and the P(winning game 2)= 25%, and 30%-25% = 5%
Game 1: P (yellow or blue) = 3/10 = .30
Game 2: P(tails and odd) = P(T1 or T3) = 2/8 = 1/4 =.25