Joanie got money from her uncle on every birtday. The amount of money he gives h

Question

Joanie got money from her uncle on every birtday. The amount of money he gives her is equal to her new age. ( when she turned 5 she gave her $5, when she turned 7 she gave her $7 etc.) she always put the money in a special box, rather than spend it. A) how much did she have in the box the day after her 18th birthday? B) she now has $ 2,145 in the box how old is she? Joanie got money from her uncle on every birtday. The amount of money he gives her is equal to her new age. ( when she turned 5 she gave her $5, when she turned 7 she gave her $7 etc.) she always put the money in a special box, rather than spend it. A) how much did she have in the box the day after her 18th birthday? B) she now has $ 2,145 in the box how old is she? A) how much did she have in the box the day after her 18th birthday? B) she now has $ 2,145 in the box how old is she?

Explanation / Answer

A)

after 18 years she has money in box is = 1+2+3+.........+18

= 18(18+1)/2 from sum of n numbers

= $ 171

B)

given after n yearsn she has $2145

If she is n years old, the money she would have got so far =
1+2+3+4....+n = 2145
The left side is an arithmetic progression with 1st term as 1, difference as 1 and n terms. (It is in fact the sum of the 1st n integers starting from 1)

ie n(n+1)/2 = 2145

Simplifying, n2 + n - 4290=0
Factorizing: (n+66)(n-65) = 0
n = -66, or n = 65.
Since age cannot be negative, Joanie is 65 years old.

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