A group of students can complete a project in 12 days. If 4 more students join, they can complete it in 8 days. How many students were initially in the group?
Practice Questions
1 question
Q1
A group of students can complete a project in 12 days. If 4 more students join, they can complete it in 8 days. How many students were initially in the group?
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Let the initial number of students be x. The work done is inversely proportional to the number of days. Setting up the equation gives x = 10.
Questions & Step-by-step Solutions
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Q
Q: A group of students can complete a project in 12 days. If 4 more students join, they can complete it in 8 days. How many students were initially in the group?
Solution: Let the initial number of students be x. The work done is inversely proportional to the number of days. Setting up the equation gives x = 10.
Steps: 9
Step 1: Let the initial number of students be x.
Step 2: The group can complete the project in 12 days, so the total work can be represented as 'work = students * days'. This means the total work is x * 12.
Step 3: When 4 more students join, the total number of students becomes x + 4.
Step 4: With the new group of students, they can complete the project in 8 days. So, the total work is also (x + 4) * 8.
Step 5: Since the total work remains the same, we can set the two expressions for work equal to each other: x * 12 = (x + 4) * 8.
Step 6: Expand the equation: 12x = 8x + 32.
Step 7: Subtract 8x from both sides: 12x - 8x = 32, which simplifies to 4x = 32.
Step 8: Divide both sides by 4 to find x: x = 32 / 4, which gives x = 8.
Step 9: Therefore, the initial number of students in the group is 8.
