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gum pack costs

by kanha81 » Sat May 30, 2009 1:46 pm
Inflation is roaring in the Selva Republic. The price of a pack of gum has increased 5 Pesos per year every year since 1996. If 10 packs of gum were purchased every year from 2004 to 2008, the total cost would be 3500 Pesos. How many Pesos did a single pack of gum cost in 2001?

A) 52
B) 48
C) 25
D) 45
E) 35

Any faster way to solve this problem?
Last edited by kanha81 on Sat May 30, 2009 2:56 pm, edited 1 time in total.
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by dmateer25 » Sat May 30, 2009 2:25 pm
Let x = gum in 2004

10x
10x + 50
10x + 100
10x + 150
10x + 200

50x + 500 = 3500
50x = 3000
x = 60

2003 = 55
2002 = 50
2001 = 45


I get 45
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by kanha81 » Sat May 30, 2009 2:37 pm
dmateer25 wrote:Let x = gum in 2004

10x
10x + 50
10x + 100
10x + 150
10x + 200
Just so that I understand-
The reason you're adding 50 is because every year the gum pack increases by 5 pesos, hence a 10 gum pack would increase by 50 pesos every year. It may look trivial, but I want to make sure that I am understanding the logic properly. Please respond.
dmateer25 wrote: 50x + 500 = 3500
50x = 3000
x = 60

2003 = 55
2002 = 50
2001 = 45


I get 45
Nice! Thanks.
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by dmateer25 » Sat May 30, 2009 2:46 pm
Just so that I understand-
The reason you're adding 50 is because every year the gum pack increases by 5 pesos, hence a 10 gum pack would increase by 50 pesos every year. It may look trivial, but I want to make sure that I am understanding the logic properly. Please respond.
Yep, exactly!
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by raleigh » Sat May 30, 2009 2:50 pm
Look at it like this:
year: cost
2004: 10x
2005: 10(x+5) = 10x + 50
2006: 10(x+5+5) = 10x + 100
2007: 10(x+10+5) [x + 10 was the price in 2006]
.
.
.

What was answer D supposed to be? I got 45, too, but it isn't an answer.
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by kanha81 » Sat May 30, 2009 2:57 pm
raleigh wrote:Look at it like this:
year: cost
2004: 10x
2005: 10(x+5) = 10x + 50
2006: 10(x+5+5) = 10x + 100
2007: 10(x+10+5) [x + 10 was the price in 2006]
.
.
.

What was answer D supposed to be? I got 45, too, but it isn't an answer.
Apologies for the typo..I have edited the answer choice
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