THE TOTAL AGE OF GROUP OF PARENTS IS 342.A NEW PARENT AGED 48 JOINS THE GROUP AND THE AVERAGE RISES BY 1. WHAT IS THE ORIGINAL AVERAGE.
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Sra
let there be n parents
The average age at first is 342/n
After adding 1 parent and 48 years, the new average is 390/(n+1)
342/n + 1 = 390/(n+1)
342(n+1) + n(n+1) = 390n
342n + 342 + n + n^2 - 390n = 0
n^2 - 47n + 342 = 0
342 = 2*171 = 2*3*57 = 2*3*3*19
(n-38)(n-9) = 0
so there were either
38 parents average 9 years old (not likely), or
9 parents average 38 years old
when a 48-year old joins, there are now 10 parents avg age 39
To find the original average age of the group of parents, we can follow these steps:
1. Let's assume the original average age of the group of parents is 'x'.
2. The total age of the group of parents is given as 342. So, the sum of all their ages is 342.
3. The number of parents in the group is not given explicitly, but we don't need it to find the original average age. We are only interested in the change in the average, not the specific number of parents.
4. After a new parent aged 48 joins the group, the average age rises by 1. This means the new average is 'x + 1'.
5. We can now set up an equation using the information: (Sum of all ages) / (Number of parents) = (New average age)
(342 + 48) / (Number of parents + 1) = (x + 1)
6. Simplifying the equation, we get:
(342 + 48) = (x + 1) * (Number of parents + 1)
390 = (x + 1) * (Number of parents + 1)
7. Since we don't have the exact number of parents, we cannot solve for 'x' directly. However, we can determine the value of 'x' in terms of the number of parents. Let's represent the number of parents as 'n'.
390 = (x + 1) * (n + 1)
390 = xn + x + n + 1
389 = xn + x + n
8. Without further information about the number of parents, we can't calculate the exact value of 'x'. However, we can express the original average age as:
x = (389 - n) / (n + 1)
The original average age depends on the specific number of parents in the group.