Number Problems
Two numbers add up to 6. One is 2 more than the other. What are the numbers?
So, the numbers are 2 and 4
You have 20 coins in nickels, dimes, and quarters. The total value is $2.65. You have twice as many dimes as nickels. How many of each coin do you have?
N=6
D=12
Q=2
A square has a perimeter of 16 cm. What is the length of one side?
Perimeter = 4 × side → 4s = 16 → s = 4 cm
You deposit $10 at 10% simple interest for 1 year. How much interest?
$1
In a right triangle, one of the angles is θ, and the opposite side is 5 units while the adjacent side is 12 units.
Find:
1. tan(θ)
2. sin(θ)
3. cos(θ)
tan(θ) = 5 / 12
sin(θ) = 5 / 13
cos(θ) = 12 / 13
The sum of these three numbers x,x+2,x+4 is 216 what is the number?
x=70
You have 20 coins, all dimes and quarters, worth $3.20. How many of each do you have?
18 quarters and 12 dimes
A triangle has sides of length 7 cm, 24 cm, and 25 cm. Prove that it is a right-angled triangle, and then find its area.
84 square cm.
Blue jays star Bo Bichette earned 12 million last season. Suppose he invests his $12 million in an account earning 5% compound interest annually.After 2 years, he must pay 30% income tax on the interest earned only. How much will he have after 2 years?
Bo Bichette will have $12,861,000 after 2 years.
A ladder is leaning against a wall. The ladder is 12 feet long and makes a 60° angle with the ground. How high up the wall does the ladder reach?
The ladder reaches about 10.39 feet up the wall.
The sum of two numbers is 72. One number is 3 times the other. What are the numbers?
18 and 54
Emma has a total of 40 coins made up of pennies (1¢), nickels (5¢), and dimes (10¢). The number of pennies is twice the number of dimes, and the total value of all the coins is $2.00. How many of each type of coin does she have?
Final Answer: d = 0 (dimes) p = 0 (pennies) n = 40 (nickels)
The length of a rectangle is 3 m more than twice the width. The area is 65 m². Find the dimensions.
The width is 5 m and the length is 13 m.
You invest $1,030 in a savings account that earns 7.4% simple interest per year. How much interest will you earn after 2 years?
$1,152.44
A hamster is on the hamster wheel. The wheel’s diameter is 10 cm, and it made 40 rotations from its original point in 1 minute. To the nearest centimeter, how far has the original point traveled in 5 seconds?
s≈105cm
The total length of two walls is 30ft, one wall is twice the length of the other wall. What are the lengths of the walls?
The shorter wall is 10ft
The longer wall is 20 ft
You have 8 coins made up of nickels (5¢) and dimes (10¢). If the total value is 60 cents, how many of each coin do you have?
Nickels = 4, Dimes = 4
Ian wants to change the position and size of his octagonal swimming pool at coordinates A(-4,2), B(-4,-2), C(-2,-4), D(2,-4), E(4,-2), F(4,2), G(2,4), H(-2,4). He translates his pool 7 units right and 4 units down, later he enlarges the pool by a factor of 2. Find the coordinates of the vertices of the image.
The new coordinates are A’(6,-4), B’(6,-12), C’(10,-16), D’(18,-16), E’(22,-12), F’(22,-4), G’(18,0), H’(10,0).
Derek invests $2,000 in a savings account that earns 5% simple interest per year. How much interest will he earn after 3 years?
Derek will earn $300 in interest after 3 years.
A park ranger whose eye level is 5 ft above the ground measures the angle of elevation to the top of an eruption of Old Faithful geyser to be 30. If the ranger is standing 200 ft from the geyser’s base, what’s the height of the eruption to the nearest foot?
115.4 ft
At a bookstore, a customer buys two types of books: novels and comic books. She buys a total of 24 books, and she buys 4 more novels than comic books. How many novels and how many comic books did she buy?
She bought 14 novels and 10 comic books.
Mario has a total of 30 coins made up of quarters and dimes, worth $5.10 in all. How many of each coin does she have?
Mario has 14 quarters and 16 dimes.
The length of a rectangle is 5 cm more than twice its width. If its perimeter is 58 cm, what are its dimensions?
Width = 8 cm, Length = 21 cm
You invest $1,000 at 5% annual interest, compounded annually, for 3 years.
$1157.6
A ladder is leaning against a wall. The ladder is 10 feet long and makes an angle of 65° with the ground. How high up the wall does the ladder reach?
The ladder reaches approximately 9.1 feet up the wall.
A theater sold 80 tickets. Adult tickets cost $10 and Child tickets cost $5 The total amount collected was $600. How many adult and how many child tickets were sold?
both child and adult tickets got sold 40 each
A cashier has a total of 50 coins, made up of dimes (10¢) and pennies (1¢). The total value is $2.30. How many dimes and how many pennies does the cashier have?
20 dimes and 30 pennies
Lewis comes to a triangle violet garden that has corners that are 60 degrees and the all sides are 7 cm long. Find the area of the triangle.
12.25 cm^2
Samantha deposits $2,500 into a savings account that earns 4.8% simple interest annually. She plans to leave the money in the account for 3 years. How much interest will she earn, and what will be the total amount in the account at the end of 3 years?
$360
Two hikers, Emma and Leo, start from the same point at the base of a mountain. Emma hikes 7 km directly north, and Leo hikes 10 km heading 60° east of north. They both stop to rest. How far apart are Emma and Leo after their hikes?
about 8.89 km.