Lower Elementary
Question: Franklin had a full box of cookies in the morning. After lunch he ate 1/5 of the cookies in the box. The number of cookies Franklin ate was 4 cookies. How many cookies were in the box when it was full?
Answer: 20 cookies
Note: Franklin ate 1/5 of the cookies in the box. This number of cookies he ate is the same number found in each part when you take the cookies in the box and divide the cookies into 5 equal parts. Since Franklin ate 4 cookies, that means the amount of cookies in each of the 5 equal parts is 4. To find the total amount of cookies in the box when it was full add up the cookies in each of the 5 parts. 4 + 4 + 4 + 4 + 4 = 4 x 5 = 20 cookies.
Upper Elementary
Question: 12 identical toy robots cost a total of $180. What would the total cost of 8 of these toy robots be?
Answer: $120
Note: To find the cost of 8 toy robots, first find the cost of one toy robot and then multiply that value by 8.
Since 12 identical toy robots cost a total of $180, to find the cost of one robot divide 180 by 12.
180 / 12 = 15
Each toy robot costs $15. The cost of 8 toy robots is 8 x 15 = 120. So 8 toy robots cost $120.
Middle School
Question: A basketball team played 96 games during its season. The team won five times as many games as they lost. How many games did the basketball team win?
Answer: 80 games
Note: This problem can be solved using either the guess and check method or algebraically.
Algebraic solution:
The sum of the games won and the games lost equals the total games played.
games won + games lost = total games
We know the team won 5 times as many games as they lost and the total games played is 96.
Since we don’t know how many games they lost we can let the number of games lost = x. That means the number of games won = 5x
So the equation is:
5x + x = 96
Solving we find:
5x + x = 96
6x = 96
x = 16 (games lost)
To find the number of games the team won multiply the number of games lost (16) by 5. 5 x 16 = 80.
Algebra and Up
Question: The three angles of a triangle are in the following ratio 3:4:5, what is the measure of the largest angle?
Answer: 75 degrees
Note: The sum of the angles in a triangle is 180 degrees. Using this fact with the the ratio of the angles we can set up an equation to solve for the largest angle.
Because the three angles are in the ratio 3:4:5 that means there is a value x so that 3x + 4x + 5x = 180, where
3x = measure of the smallest angle; 4x = measure of the middle angle; 5x = measure of the largest angle
Solving the equation, we find:
3x + 4x + 5x = 180
12x = 180
x = 15
3 * 15 = 45 degrees (smallest angle)
4 * 15 = 60 degrees (middle angle)
5 * 15 = 75 degrees (largest angle)
