The sum of the ages of a group of friends is 250 years.
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The sum of the ages of a group of friends is 250 years. If you add 4 years to each of their ages, their total combined age becomes 282 years. How many friends are in the group?
Show answer & explanation
If there are n friends and each person's age increases by 4 years, the total age increases by 4n years. Since the total increases from 250 to 282, we have 4n = 32, so n = 8. There are 8 friends in the group.
Step-by-step Derivation:
Let n = number of friends.
Initial condition: Sum of all ages = 250
After adding 4 years to each person's age:
- Each person's age increases by 4
- Total age increase = 4 × n (since there are n people)
- New sum = 250 + 4n = 282
Solving for n:
4n = 282 - 250
4n = 32
n = 32 ÷ 4
n = 8
Verification:
Original total: 250 years
Increase per person: 4 years
Total increase: 4 × 8 = 32 years
New total: 250 + 32 = 282 years ✓