# Help me solve this word problem....

Discussion in 'The Guru's Pub' started by J.B.west, Sep 24, 2014.

1. ### J.B.westBanned

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Ok so Im not too good at algebra or math for that matter...but Im trying to help my friends kid solve this word problem...

A group of 19 students want to see the show at the planetarium. Tickets cost 11 for members and 13 for non members.

The membership costs \$5 per year. Write an equation that can be used to determine n, the number of visits per year for which the cost of being a members is equal to the cost of a non member.

2. ### ClouseauAncient Guru

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11n + 5 = 13n

How does one visit 2.5 times?

Last edited: Sep 24, 2014
3. ### XP-200Ancient Guru

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They were in a combine harvester accident and lost both legs. 4. ### scoter man1Ancient Guru

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They generally do that in early algebra to see if you understand that you need to round up to the nearest whole number for that kind of problem.

5. ### ClouseauAncient Guru

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Been in finance too long to remember that far back. Son, 3rd grade, came home with math homework one night last year and had a hard time understanding why multiplication is being introduced by use of arrays. Showed him the "old school" way and he picked it up in nothing flat.

6. ### AsiJuAncient Guru

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That's actually the simplified form FYI @OP.

As there are 19 students, each for which the membership costs 5, then we get:

19(11n + 5) = 19(13n)

where n is the number of visits (and 11 and 13 are the cost per visit for member / non-member respectively).

Indeed the 19's cancel out, which furthermore means the number of students is insignificant to the solution (OP mention this if you want to impress Solving for n gives 2.5, meaning only two or one visits a year and membership doesn't profit.

3 or more visits per year and it's better to become members.

EDIT: if you solve (algebraically) for n, you get n = 5 / 2.
So that's the simplest equation for the given assignment.

Last edited: Sep 24, 2014
7. ### ArctucasAncient Guru

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One visit for a member is actually 16 (11+5), two visits is 27 (2x11+5), three visits equals 38 (3x11+5).

One visit for a non-member is 13, two visits is 26, three visits is 39.

So, 3 (3x11+5=38) and 1/11 (of the 11 member admission charge = 1) visits for a member would equal the 39 the non-member pays.

8. ### J.B.westBanned

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the equation is 11n + 5=13n

you are way off...its not like the member pays an extra 5 bucks each time they go, its a one time deal. You need to spread the 5 dollars into the amount of times the member goes to match the amount it would cost the same with a nonmember....

9. ### AsiJuAncient Guru

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-removed-

Last edited: Sep 25, 2014
10. ### ArctucasAncient Guru

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Of course, the 5 is a one-time fee, but it must be accounted for in the total cost, no?

The answer should be 3, there is no ½ visit.

Last edited: Sep 25, 2014

11. ### J.B.westBanned

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The problem is that it specifically says, "the number of visits per year for which the cost of being a members is equal to the cost of a non member". Equal means that the answer is 2.5, if it asked "what is the minimum number of times a student would have to go for it to be worth the membership cost?" then 3 is the answer.

12. ### ArctucasAncient Guru

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OK, let me know how that ½ visit works?

13. ### NoviceReiAncient Guru

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Being that it's a math problem, the strict answer is 2.5 (although the practical answer is 3).

Eitherway, any sensible professor/teacher would accept both as correct.

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