Solve the following real-world problem: Ahmadullah's basketball team will play 21 games this season. That is 12 more games than 1 over 3 the number of games they played last season. How many games did they play last season?
Let's denote the number of games they played last season as x.
According to the problem, Ahmadullah's basketball team will play 21 games this season.
The number of games they played this season is 12 more than 1/3 of the number of games they played last season, which can be written as:
x + 12 = (1/3)x
To solve for x, we multiply both sides of the equation by 3 to eliminate the fraction:
3(x + 12) = x
3x + 36 = x
2x = -36
x = -36/2
x = -18
However, the number of games cannot be negative, so this solution is not valid.
Therefore, there is no solution for this problem.
Let's solve the problem step by step:
Step 1: Set up an equation to represent the given information.
Let the number of games played last season be "x."
According to the problem, Ahmadullah's basketball team will play 21 games this season, which is 12 more games than 1 over 3 of the number of games they played last season. So we can write the equation as:
21 = x + (1/3)x + 12
Step 2: Simplify the equation.
To simplify the equation, we need to combine like terms. Since the denominators are 1 and 3, we can rewrite the equation with a common denominator of 3:
21 = (3/3)x + (1/3)x + 12
21 = (4/3)x + 12
Step 3: Isolate the variable.
To isolate the variable x, we need to get rid of the constants on the right side of the equation. We can do this by subtracting 12 from both sides:
21 - 12 = (4/3)x
9 = (4/3)x
Step 4: Solve for x.
To find the value of x, we need to multiply both sides of the equation by the reciprocal of (4/3), which is (3/4):
(9)(3/4) = x
27/4 = x
Step 5: Simplify the answer.
The fraction 27/4 can be expressed as a mixed number: 6 remainder 3. So the team played 6 games last season.
Therefore, Ahmadullah's basketball team played 6 games last season.
To solve this real-world problem, we need to find the number of games Ahmadullah's basketball team played last season.
Let's break down the information given:
- This season, the team will play 21 games.
- This season, they are playing 12 more games than 1 over 3 of the number of games they played last season.
Let's set up an equation to represent the problem:
Number of games this season = 1/3 * Number of games last season + 12
We are trying to find the number of games they played last season, so let's solve the equation.
21 = 1/3 * Number of games last season + 12
To isolate the variable, we subtract 12 from both sides:
21 - 12 = 1/3 * Number of games last season
9 = 1/3 * Number of games last season
Now, to solve for the number of games last season, we need to multiply both sides of the equation by 3, because 3 * 1/3 = 1:
9 * 3 = 1/3 * Number of games last season * 3
27 = Number of games last season
Therefore, Ahmadullah's basketball team played 27 games last season.