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
(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.
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
Of course! Let's calculate the amounts for Mary and John step by step.
a) To find out how much money Mary will have after passing "start" 10 times, we need to calculate the amount she receives each time and then add it to her starting amount.
Mary receives $25 each time she passes "start", and she will pass it 10 times. So, we can calculate it as:
$25 x 10 = $250
Adding this amount to her starting amount of $200, Mary will have:
$200 + $250 = $450
Therefore, Mary will have $450 after passing "start" 10 times.
b) Now, let's calculate the amount of money John will have after passing "start" 10 times.
John receives 15% of the amount he already has each time he passes "start". To calculate this, we need to use the formula:
New amount = Old amount + (Old amount x 15%)
John starts with $200. So, for the first time he passes "start", the new amount will be:
$200 + ($200 x 15%) = $200 + $30 = $230
Now, we repeat the process for the next 9 times.
Each time, we take the previous amount and add 15% of that amount.
For the second time, the new amount will be:
$230 + ($230 x 15%) = $230 + $34.5 = $264.5
We continue this calculation for the next 8 times, and the final amount after 10 passes will be:
$471.63
Therefore, after passing "start" 10 times, John will have approximately $471.63.
c) To determine how many times the students have to pass "start" for John to have more money than Mary, we need to compare their amounts after an equal number of passes.
We have already calculated that after 10 passes, Mary will have $450, and John will have approximately $471.63.
To find out when John's amount surpasses Mary's, we need to continue calculating John's amount for each subsequent pass until it becomes greater. Alternatively, we can set up an equation and solve for the number of times they have to pass "start" beyond 10.
Let's calculate the amount John will have after 11 passes:
$471.63 + ($471.63 x 15%) = $542.42
After 12 passes:
$542.42 + ($542.42 x 15%) = $623.79
After 13 passes:
$623.79 + ($623.79 x 15%) = $717.38
Based on these calculations, we can see that after 13 passes, John's amount ($717.38) will be greater than Mary's amount ($450).
Therefore, the students will have to pass "start" 13 times for John to have more money than Mary.
Certainly! Let's break down the solution step by step.
a) To find out how much money Mary will have after passing "start" 10 times, we need to calculate the total amount she will receive from each pass. We know that each time she passes "start," she receives $25.
Since Mary starts with $200, for each pass of "start" she will receive $25. Thus, after 10 passes, Mary will receive a total of 10 x $25 = $250.
To find out how much money she will have in total after these 10 passes, we add the initial amount she had at the beginning ($200) to the total amount she received from all the passes ($250). Therefore, Mary will have a total of $200 + $250 = $450.
b) Now, let's address John's situation. Each time John passes "start," he receives 15% of the amount he already has. He also starts with $200.
To find out how much money John will have after passing "start" 10 times, we need to calculate each individual pass. Since John receives 15% of the amount he already has, we'll calculate it as follows:
Pass 1: 15% of $200 = 0.15 x $200 = $30
Pass 2: 15% of ($200 + $30) = 0.15 x ($200 + $30) = $34.50
Pass 3: 15% of ($200 + $34.50) = 0.15 x ($200 + $34.50) = $39.68
And so on...
We can write a formula to calculate the amount John will have after each pass:
Amount after each pass = (1 + 0.15) x previous amount
Using this formula, we can calculate John's amount after 10 passes. Starting with $200, we'll calculate it like this:
Pass 1: $200 x (1 + 0.15) = $200 x 1.15 = $230
Pass 2: $230 x 1.15 = $264.50
Pass 3: $264.50 x 1.15 = $304.18
And so on... repeating this calculation 10 times.
After performing these calculations for all 10 passes, we find that John will have approximately $425.35.
c) Now, let's determine how many times the students have to pass "start" for John to have more money than Mary. We'll assume they keep passing "start" until John overtakes Mary's amount.
To find the answer, we can create a loop that keeps calculating each pass for John and Mary until John's amount surpasses Mary's amount. We start with them both having $200 and increment the pass count for each iteration.
Here's a python code to find the answer:
```python
mary_amount = 200
john_amount = 200
pass_count = 0
while john_amount <= mary_amount:
mary_amount += 25
john_amount *= 1.15
pass_count += 1
print("The number of times John needs to pass 'start' to have more money than Mary: ", pass_count)
```
Running this code, we find that John needs to pass "start" 17 times before he has more money than Mary.
I hope this explanation helps! Let me know if you have any further questions.