Mixed Topics
Pencils come in packages of 10. Erasers come in packages of 12. Phillip wants to purchase the smallest number of pencils and erasers so that he will have exactly 1 eraser per pencil. How many packages of pencils and erasers should Phillip buy?
Phillip should buy 6 packages of pencils and 5 packages of erasers.
There are 2 numbers whose sum is equal to 72. One number is twice the other number. What are the numbers?
The numbers are 24 and 48
A rectangular garden is 6 meters longer than it is wide. The area of the garden is 16 square meters. Find the length and width of the garden.
The garden is 2 meters wide, and its length is 8 meters.
A triangle has a perimeter of 50. If 2 of its sides are equal and the third side is 5 more than the equal sides, what is the length of the third side?
The length of third side is 20
The length of a rectangular field is 3 meters more than the width. The area is 108 meters squared. Find the dimensions of the field.
The field is 12 meters long and 9 meters wide
The product of two positive consecutive even integers is 528. Find the value of each integer.
The two integers are 22 and 24.
Jordan is 2 years older than his brother James. If the product of their ages is one less than five times the sum of their ages, how old are Jordan and James?
Jordan is 11 years old and James is 9 years old.
The perimeter of a rectangle is 30 centimeters, and the area is 54 square centimeters. Find the width and length of the rectangle. [Hint: Let w represent the width; then 15 - w represents the length.]
The dimensions of the rectangle are 6 x 9 cm.
The base of triangle is 5 cm less than twice the height. If the area is 75 square cm, then what is the length of the base and the height?
The height measures 10 cm and the base measures 15 cm.
The width of a rectangle is 3 feet less than its length. The perimeter of the rectangle is 110 feet. Find its dimensions.
The dimensions of the rectangle are 26 and 29.
Rosie and Mark are twins and today is their birthday. Rosie has brought 24 gummy bears to share in class and Mark has brought 18 candy bars. If they want to share their candy with their friends in such a way that all their friends have the same amount of each type of candy and they give out as much candy as possible, how many friends could they give candy to?
Each one of the 6 friends that are going to get candy from Rosie and Mark are going to get 4 gummy bears and 3 candy bars.
The length of a rectangle swimming pool is 2 yards more than 2 times the width. The area of the pool is 144 square yards. Find the dimensions of the pool.
The pool is 8 yards by 18 yards
The longer leg of a right triangle is one unit shorter than twice the length of the shorter leg. The hypotenuse is one unit longer than twice the length of the shorter leg. Find the lengths of the three sides of the triangle.
The dimensions of the triangle are 8 cm, 15 cm and 17 cm.
The height of a triangle is 4 inches more than twice the length of the base. The area of the triangle is 35 square inches. Find the height of the triangle.
The height of the triangle is 14 inches.
A rectangle is 4 times as long as it is wide. If the length is increased by 4 inches and the width is decreased by 1 inch, the area will be 60 square inches. What are the dimensions of the original rectangle?
The width of the original rectangle is 4 inches. The length of the original rectangle is 16 inches.
An apple orchard contains 84 trees. The number of trees per row is 5 more than the number of rows. Find the number of rows.
The length of a rectangular vegetable garden is 4 feet more than its width. After a 2 foot cement border is placed around the garden, the area of garden and border is 320 square feet. Find the original dimensions of the vegetable garden.
The garden is 12 feet by 16 feet.
The sum of the areas of a square and a rectangle is 64 square centimeters. The length of the rectangle is 4 centimeters more than a side of the square, and the width of the rectangle is 2 centimeters more than a side of the square. Find the dimensions of the rectangle and the square.
The side of the square is 4 cm and the dimensions of the rectangle are 8 x 6 cm.
If a triangle's height is 4 inches less than two times it's base, and has an area of 120 square inches. What is the height of the triangle?
The height of the triangle is 20 inches.
The sum of the areas of a square and a rectangle is 64 squared cm. The length of the rectangle is 4 cm more than the side of the square, and the width of the rectangle is 2 cm more than the side of the square. Find the dimensions of the rectangle and the square.
The square has a length and width of 4, while the rectangle has a length of 8 and a width of 6.
The product of two consecutive odd whole numbers is one less than five times their sum. Find the numbers.
The numbers are 2 and 11.
The formula for the number of games to be played in a football league where each team is to play each other twice is N = x2 - x, where x is the number of teams in the league and N is the number of games to be played. If a league wants to limit the games to a total of 132 games, how many teams can be in the league?
The league needs to have 12 teams.
An apple orchard contains 85 trees. The number of trees in each row is three less than four times the number of rows. Find the number of rows and the number of trees per row.
The orchard has 5 rows of 17 trees.
Before she goes camping, La Verne has to buy a tent pole to replace the one she lost on her last outing. If the area of the front of the tent is 22 square feet and the base of the tent has the dimensions indicated below, how tall must the pole be?
The pole should be 5.5 feet long.
In a quadrilateral 2 angles are equal. The third angle is equal to the sum of the two equal angles. The fourth angle is 60° less than twice the sum of the other three angles. Find the measures of the angles in the quadrilateral.
The values of the angles are 35°, 35°, 70° and 220°