Two students, Mary and John, play a game. Each time Mary passes “start” she received $25. Each time John passes “start” he receives 15% of the amount he already has. Both students start with $200.

Question

Two students, Mary and John, play a game. Each time Mary passes “start” she received $25. Each time John passes “start” he receives 15% of the amount he already has. Both students start with $200.
a. How much money will Mary have after she has passed “start” 10 times?
b. How much money will John have after he has passed “start” 10 times?
c. How many times will the students have to pass “start” for John to have more money than Mary?

a) 450$
b) could you please help me? Thank you so much

Steve · Accepted Answer

(a) 200+25*10 = 450 -- you are correct
(b) 200*1.15^10 = 809.11
(c) Hmm. seems kind of odd. If you tabulate the amounts held after n passes,
n Mary John
0 200 200
1 225 230
John has more after a single pass, and gains faster and faster on every pass thereafter. You sure that rate is 15% ? Any rate greater than 12.5% will keep john always ahead of Mary.

Lucas · Answer

Dear Steve, thank you so much for your really so huge help.
I only wanted to ask you and I'm sure I'm wrong about it but Both students start with $200 and both how much money will have after they have passed START 10 times.
I did:
I used formula : un =u1+(n-1)d arithmetic seq.
200 + (11-1)25 = 450 $

for b) un =u1r^n-1
200(1+0,15)^11-1
= 809,11 + 200
= 1009,11 $

but I'm sure , it is wrong , you are yousing formlula compound interest, right for b? Not geometric sequence?

for c) it looks there are some mistake in the school book

Thank you so so much for answer.
Have a very nice day