Number Problems
Coin/Money Problem
Geometry Problem
Percent or Interest Problem
Trigonometry Problem
100
Gigi has 18 coins: nickels and quarters. Total = $2.10. How many of each?
12 nickels, 6 quarters
100
Maria has 15 coins consisting of quarters and dimes. The total value is $2.70. How many quarters and dimes does she have?
8 Quarters and 7 Dimes
100
A rectangle has a length that is 5 feet more than twice its width. If the perimeter is 46 feet, find the dimensions.
The width is 6 feet, and the length is 17 feet.
100
Jamal invests $1,500: part at 3%, rest at 5%. Earns $66 in interest. How much at each rate?
$450 at 3%, $1,050 at 5%.
100
From a point 50 feet from the base of a building, the angle of elevation to the top is 35°. Find the height of the building.
35.01 feet
200
The sum of three consecutive even integers is 84. Find the three integers.
The integers are 26, 28, and 30
200
Elsa and Anna sold 30 tickets for an event. Tickets for children cost $1.50 and tickets for adults cost $2.00. Total receipts for the event were $50.00. How many of each type of ticket was sold?
20 children tickets and 10 adult tickets were sold
200
The length of a rectangle is 2 more than its width. If the area is 15 square feet, find the dimensions.
The length is 5 units and width is 3 units
200
An investment of $5000 earned $350 in simple interest over 2 years. What was the annual interest rate?
3.5% rate
200
From the top of a 20 m tall lighthouse, a sailboat is sighted at an angle of depression of 40°. How far from the lighthouse is the boat?
16 meters
300
The sum of two numbers is 50. Their difference is 18. What are the numbers?
Numbers are 34 and 16
300
Michaela has $2.05 in dimes and nickels in her change purse. She has seven more dimes than nickels. How many coins of each type does she have?
Michaela has 9 nickels and 16 dimes.
300
A rectangular garden has an area of 96 square meters. Its length is 4 meters more than its width. Find the dimensions.
● Width = 8 m
● Length = 12 m
300
John invested $5000, part at 4% interest and the rest at 6%. If he earns $260 in interest in one year, how much was invested at each rate?
● $2000 at 4%
● $3000 at 6%
300
A ladder leans against a wall. It reaches 10 feet up the wall and forms a 65° angle with the ground. How long is the ladder?
The ladder is approximately 11.04 feet long
400
A basketball player shoots a ball, and the height of the ball (in feet) after ttt seconds is modeled by the quadratic equation: h(t)=−16t^2 + 20t + 6, where h(t) = height of the ball in feet and t = time in seconds after the shot.
1. How long does it take for the ball to hit the ground?
2. What is the maximum height the ball reaches?
The ball hits the ground at t=1.5 seconds.
Maximum height is 12.25 feet at 0.625 seconds.
400
The population of a small town was 12,000 in the year 2020. The population grows by 3% each year.
What will the population be in the year 2026?
The town’s population will be approximately 14,329 in 2026.
400
An architect is designing a triangular glass rooftop for a greenhouse. The rooftop will be a non-right triangle, shaped like triangle ABC:
● Side AB=18 ft
● Side AC=26 ft
● The angle between them, ∠A=47 degree
1. What is the length of side BC, the base of the triangle?
2. What are the measures of the other two angles, ∠B and ∠C?
● BC ≈ 19.01ft
● ∠B ≈ 90
● ∠C ≈ 43
400
Jenna invests $4,000 in an account that earns 4% annual interest, compounded semiannually. She plans to leave the money untouched for 3 years. How much money will Jenna have in her account after 3 years?
Jenna will have approximately $4,504.64 after 3 years.
400
A homeowner wants to install a solar panel on their roof. To maximize efficiency, the panel should be tilted at an angle equal to the latitude of their location, which is 35°. The panel will be mounted on a rectangular support frame where:
● The base of the frame is 4 feet long.
● The tilted panel forms the hypotenuse of a right triangle.
● The height of the support (vertical leg) is unknown and labeled as hhh.
Because the panel is 4 feet wide, it must fit on the frame such that its actual length along the panel surface is no more than 5 feet.
1. Whether a 35° angle will allow the solar panel to fit within the 5-foot surface length.
2. If not, what is the maximum angle the homeowner can use while still using the 5-foot-long panel?
3. What is the height of the triangle frame at 35°?
1. Yes, a 35° angle works — the panel will be 4.885 ft, which is < 5 ft.
2. Maximum angle before exceeding the panel length: 36.87°
3. Height of frame at 35°: ≈ 2.81 ft
500
Find the sum of the question:
Σ(3𝑘^2−2𝑘+4), where k=1 to n.
The sum is 𝑛(2𝑛^2+𝑛+7)/2
500
Find the area of the circle.
The area of the circle is 1225π unit.
500
In a restaurant there are three different types of meats, beef, pork, and chicken, also three different types of veges, broccoli, cabbage, spinach. The chef wants to use up all these materials to make a three dish meal, each dish can use one or more materials to cook, and each type of materials can only be used once, also each dish must include meat. How many ways can he cook?
27 different types of separating