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[Dental2000]

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It is just me or r these questions kinda annoying?

1) John does Laundry once a week on Wednesdays and Jogs on all even numbered days. If he cleans his apartment every 5 days and it was last cleaned on Tuesday, June 1st. How many days after this date will he do all 3 activities on the same day?

2) Ken can buy record albums for 5.99$ at a store which is within walking distance from his house or he can take the subway to the discount store where records cost 5.50$. Subway fare is .75$ in each direction. What is the least number of records he can buy so that his savings on his records will be greater than the cost of riding to and from the station?

3) The prices in a penny arcade are worth 5 cents, 50 cents and 2.00$. The game costs 25 cents and pays out half the amount on the average. If one prize is awarded for each 25 cents games and there is the same number of 50 cent prizes as there are 2.00$ prizes. How many 2.00$ prizes are their in the 160 drawings having the average pay off ?


Any help would be great, but proper explaination( a simple one would help 🙂) would be great

 

[KyoPhan]

I'll give a shot at # 2.

The cost of taking subware fare is 0.75 x 2. It is times 2 because you have to go to and back.

The savings you get for going to that discout store is 0.44 for each record. So the set up will look like this.

0.44x> 0.75(2)
x>3.4
Since you can't buy a fraction of the album, you must round up. So x=4, meaning you would have to buy 4 album.

I'll take a look at the others later.

 

[KyoPhan]

In regards to #1, I think trying to find a formula would be pretty difficult to find and time consuming. I would recommend just drawing a calendar out.

The best way to solve this I believe is to just check every Wednesday and check if all the activities will match up on that day. Wednesday the 9th doesn't match with the cleaning his apartment(He does it June first, and then every 5 days later. So on the 6th, 11th, and 16th he does it)
The next Wednesday is the 16th. This matches everything. Even date, every 5 days after the first, and is a Wednesday.

 

[toothhornet88]

In regards to #1, I think trying to find a formula would be pretty difficult to find and time consuming. I would recommend just drawing a calendar out.

The best way to solve this I believe is to just check every Wednesday and check if all the activities will match up on that day. Wednesday the 9th doesn't match with the cleaning his apartment(He does it June first, and then every 5 days later. So on the 6th, 11th, and 16th he does it)
The next Wednesday is the 16th. This matches everything. Even date, every 5 days after the first, and is a Wednesday.

Yes that's the best way BUT i would mark this question and come back to it after I've done all the others! Because it can take away some of your time more than others

 

[KyoPhan]

Yes that's the best way BUT i would mark this question and come back to it after I've done all the others! Because it can take away some of your time more than others

Agreed.
As for #3, I have no clue. The other problems seem do-able.

 

[AlbinoPolarBear]

3) The prices in a penny arcade are worth 5 cents, 50 cents and 2.00$. The game costs 25 cents and pays out half the amount on the average. If one prize is awarded for each 25 cents games and there is the same number of 50 cent prizes as there are 2.00$ prizes. How many 2.00$ prizes are their in the 160 drawings having the average pay off ?

Given
Total amount spent on games = 160*0.25 = $40.00
Total amount won in prizes = $20.00 (this is half of $40)

number of prizes = 160
number of $2.00 prizes = n
number of $0.50 prizes = n
number of $0.05 prizes = 160-2n

Total amount won in prizes
= (number of $2.00 prizes)(value of $2.00 prize) + (number of $0.50 prizes)(value of $0.50 prize) + (number of $0.05 prizes)(value of $0.05 prize)


$20.00 = n($2.00) + n($0.50) + (160-2n)($0.05)
20 = 2n + 0.50n + 8 - 0.1n
12 = 2.4n
n = 5

So..

number of $2.00 prizes = n
= 5

number of $0.50 prizes = n
= 5

number of $0.05 prizes = 160-2n
= 150

Hope this is clear.

 

[Dental2000]

Yes that's the best way BUT i would mark this question and come back to it after I've done all the others! Because it can take away some of your time more than others

true that