Word Problem: If you have 1,500,000,000 coins, how many medals can you purchase?

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Devildog1985

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Jun 25, 2019
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A Medal currently costs 1,300,000 coins
Every time a medal is purchased the cost increases by 50 coins
If you have 1,500,000,000 coins, how many medals can you purchase?
 
Devildog1985 said:
A Medal currently costs 1,300,000 coins
Every time a medal is purchased the cost increases by 50 coins
If you have 1,500,000,000 coins, how many medals can you purchase?
Click to expand...
Hint:
cost of first medal = 1300000
cost of second(2) medal = 1300000 + 1 * 50
cost of third(3) medal = 1300000 + 2 * 50
.
.
.
cost of n th medal = 1300000 + (n-1) * 50

continue...

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Yes, you can have the answer. Work it out as you have been shown.
 
No I play a game called Forge of Empires. You can buy something called forge points which, for me, currently cost 1.3 million coins. The price increases 50 coins every time you purchase. I have now how many forge points I can buy with my coins billion coins and i wanted to know how many forge points I can buy.
 
Funny I thought I could come here for a quick solution to a problem. I'm not a student. I'm an adult who is a long way from my college mathematics. I play the online game to relax. "...fries with that."? I have a very good career which does not require me doing algebra. If you don't want to assist, just don't answer. I thought this might be a friendly and supportive type of forum. I guess I was wrong. I hope you enjoy feeling superior because you know how to solve math problems.
 
The total cost \(C\) of \(n\) medals is:

[MATH]C=1300000n+25n(n-1)=25n(n + 51999)[/MATH]
And so to find how many medals you can purchase for a given amount, we equate this to that amount and solve for \(n\) and take the greatest integer less than that value (the positive root):

[MATH]25n(n + 51999)=1500000000[/MATH]
[MATH]n\approx1129.34074651919[/MATH]
And so we find that you can purchase 1129 medals.

I took you at your word that you are not a student, but we get a lot of people saying similar things in an effort to get their coursework done. That's why many of our helpers/staff are naturally suspicious. :)
 
Devildog1985 said:
Funny I thought I could come here for a quick solution to a problem. I'm not a student. I'm an adult who is a long way from my college mathematics. I play the online game to relax. "...fries with that."? I have a very good career which does not require me doing algebra. If you don't want to assist, just don't answer. I thought this might be a friendly and supportive type of forum. I guess I was wrong. I hope you enjoy feeling superior because you know how to solve math problems.
Click to expand...
Not a matter of "superior" at all. It's okay for us to establish rules of our volunteer engagement. We're mostly about helping students - and this includes the students showing some effort. Sometimes, we'll venture into other endeavors, but that would remain up to us, individually.

You've been given this. Add them up!

cost of first medal = 1300000
cost of second(2) medal = 1300000 + 1 * 50
cost of third(3) medal = 1300000 + 2 * 50
.
.
cost of n th medal = 1300000 + (n-1) * 50

n medals cost n * 1,300,000 + 50(1+2+3+...+(n-1))

Frankly, 1,300,000 is so much larger 50 one might be tempted to ignore the 50. This would create an upper bound.

1,500,000,000/1,300,000 = 15000/13 = 1,153ish -- Okay, so less than that.

1 + 2 + 3 + ... + (n-1) -- How do you suppose this might be summed?
 
MarkFL said:
The total cost \(C\) of \(n\) medals is:

[MATH]C=1300000n+25n(n-1)=25n(n + 51999)[/MATH]
And so to find how many medals you can purchase for a given amount, we equate this to that amount and solve for \(n\) and take the greatest integer less than that value (the positive root):

[MATH]25n(n + 51999)=1500000000[/MATH]
[MATH]n\approx1129.34074651919[/MATH]
And so we find that you can purchase 1129 medals.

I took you at your word that you are not a student, but we get a lot of people saying similar things in an effort to get their coursework done. That's why many of our helpers/staff are naturally suspicious. :)
Click to expand...
Thank you very much. I can understand the dilemma. Just giving the answer without the explanation might be of little use to a student. In any case I appreciate your reply.
 
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