Ratios & Proportions
A recipe requires 13 cup of flour for each 34 cup of water. How many cups of water are needed for each cup of flour?
Answer: 4/9
Which expression is not equivalent to -25?
Answer: -30--5
Yesterday, the temperature at 3:00pm was 14F. By midnight, the temperature had decreased by 18 degrees. What was the temperature at midnight?
Temperature: Start 14°F, decreased by 18°F → 14 − 18 = −4°F.
Given this data: 14, 6, 13, 17, 1, 12, 9, 18. Find the 5-number summary
Min. =
Max. =
Q1 =
Q2 =
Q3 =
What are the formulas for area of a triangle, rectangle, and a circle?
Area Formulas:
Triangle= 1/2 base x height
Rectangle= Length x Width
Circle= pi x radius squared
There are 96 pretzels in a 16-ounce bag of chocolate-covered pretzels. How many pretzels are in a 5-ounce bag?
Parking & zoo: Ms. Facio has $500. Parking $15, admission $22.95 per person. Write and solve inequality to find max number of people she can bring.
Let n = number of people (including Ms. Facio if applicable — interpret as number of people for whom admission is purchased). Total cost = parking + 22.95n ≤ 500.
Equation: 15 + 22.95n ≤ 500
Solve: 22.95n ≤ 485 → n ≤ 485 / 22.95 ≈ 21.136
An ice cream shop sold 24 vanilla milkshakes, which was 20% of all milkshakes sold that day. What was the total number of milkshakes?
Given a boxplot (min 25, Q1 30, median 35, Q3 48, max 50), determine whether there are outliers using the 1.5·IQR rule.
Boxplot: min 25, Q1 30, median 35, Q3 48, max 50
What is the formula for volume and surface area?
Volume = length x width x height
Surface Area= 2(LW + LH + WH)
Ms. Jenn paid $6.48 for 18 pencils. At this rate, how much would it cost Ms. Jenn to buy 96 pencils?
Solve and check: 3(2x − 1) = 21.
Solve: 3(2x − 1) = 21.
Answer: x = 4.
Work: 6x − 3 = 21 → 6x = 24 → x = 4.
Jayce and Jamel each open a savings account with a deposit of $200.
Jayce earned 3% simple interest per year
Jamel earned 3.2 % simple interest per year
They did not make any additional deposits or withdrawals
How much more did Jamel earn in interest than Jayce after 5 years?
Simple interest difference after 5 years
For data: 12, 15, 9, 5, 17, 16, 10, 11, 4, 8, 9, 20, 12 — find the 5-number summary and the interquartile range (IQR).
Data: 12, 15, 9, 5, 17, 16, 10, 11, 4, 8, 9, 20, 12. Answer: Min 4; Q1 8.5; Median 11; Q3 15.5; Max 20; IQR = 7.
(15x/7)+20= -1
Solve 15x/7 + 20 = −1
15x/7 = −21 → 15x =
−147 → x = −147/15 = −49/5 = −9.8
Answer: x = −49/5
Compute the unit rate: A person walks 1/2 mile in 1/4 hour. Write the unit rate in miles per hour and explain how you found it.
Unit rate: 1/2 mile in 1/4 hour → miles per hour. Answer: 2 miles per hour. Work: (1/2 mile) ÷ (1/4 hour) = (1/2) × (4/1) = 2 mph.
Write an inequality for: You earn $50 per week plus $3 per sale. You want at least $100 this week. How many sales must you make? Solve the inequality and graph the solution set on a number line.
Inequality: Earn $50 + $3s ≥ $100. Solve for s (sales). Answer: s ≥ (100 − 50)/3 = 50/3 → s ≥ 16.666... → At least 17 sales. Work: 50 + 3s ≥ 100 → 3s ≥ 50 → s ≥ 50/3 ≈ 16.67 → integer number of sales ≥ 17.
A scientist is studying the freezing temperature of two different liquids. The freezing temperature of substance A is 15 degrees lower than that of substance B. If substance B’s freezing temperature is -6 , what is the freezing temperature of substance A?
A spinner has 6 equal sectors numbered 1–6. If you spin twice, what is the probability of getting a 2 then a 5?
Spinner 1–6, spin twice: P(2 then 5).
Work: Independent spins. P(2) = 1/6, P(5) = 1/6. Multiply = 1/36.
Answer: 1/36.
Ten students from a class participated in a math quiz. The scores obtained by them are recorded as 11, 6, 7, 13, 1, 13, 16, 7, 13, 16. Find the mean, median, and mode.
Answers:
Mean 10.3
Median 12
Mode 13
U-Haul charges moving truck rental rates based on how many miles the moving trucks are driven. Their last 3 customers paid the following rates:
Ms. O paid $59.84 for 88 miles
Mr. Green paid $99.96 for 147 miles
Mr. E paid $21.76 for 32 miles
Part A: Is the relationship between the cost and miles driven a proportional relationship?
Part B How much would it cost to rent a moving truck from U-Haul to travel a total of 226 miles?
Part B — Cost for 226 miles
A rectangle has a length of (3.4x + 9.2y) and a width of (2.1x +4.7z). What is the perimeter of this rectangle?
Rectangle perimeter with length L = (3.4x + 9.2y) and width W = (2.1x + 4.7z). Perimeter P = 2L + 2W
Coach Darrel wants to buy new shoes for his 12 players.
Super Sports is offering a 20% discount on each pair of shoes, which were originally priced $72.50. A 6.5% sales tax will be applied to the discounted price.
The same shoes are also available on Double Dribble's website for $54.75. A 9% processing fee will be applied to the cost of the shoes, plus a shipping fee of $5.99 for each pair.
What is the difference in the total costs of the 12 pairs of shoes between the two stores?
Answer: $741.24
A game flips a coin then rolls a fair die. Find P(tails and 4).
Coin then die: P(tails and 4). Work: Independent events. P(tails) = 1/2. P(4 on die) = 1/6. Multiply: (1/2)*(1/6) = 1/12.
Answer: 1/12.
The dance committee has a budget of $128 to decorate the gym for the spring dance. They have already spent $65. Some members want to buy helium balloons that cost $0.80 each. Write and solve an inequality to show the number of balloons that the dance committee could buy.
Explain what your solution means in the context of the problem.
Dance committee inequality Budget $128, already spent $65, balloons cost $0.80 each. Let b = number of balloons.
Total spent ≤ 128 → 65 + 0.80b ≤ 128 0.80b ≤ 63 → b ≤ 63 ÷ 0.8 = 78.75 b must be whole number, so maximum b = 78 balloons.
Interpretation: They can buy up to 78 balloons (buying 79 would exceed the $128 budget).