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math & algebra ?

in a sport club, the annual fee for adults is $230.00 per member & for senior citizens it is $170.00. If the total annual income of the club is $129400.00, find the minimum number of senior citizens as a club member.

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Answers (5)

students who are familiar with CONGRUANCE, can solve this problem easily as shown below:
Let x be the number of regular members and y be the number of senior members. Thus:
230x + 170 y = 129,400 or
23x + 17y = 12,940 eq(1)
Using congruance notation eq(1) becomes:
23x + 17y == 12,940(mod 23)
We could use (mod 17) as well.
The symbol for congruance is three short horizontal parallel bars which I don't have on my keyboard, so I used this symbol (==) instead.
Equation (2) can be written as:
23x + 17y == (562x23 + 14) (mod 23)
but 23 == 0 (mod 23), so
0x + 17y == 1(0 + 14)(mod 23)
or 17y == 14 (mod 23) eq(3)
This means that we should add (+or - ) 23t to 14 until it becomes divisible by 17 in order to get the value of y. i.e.
y = (14 +/- 23t)/17.
for t = + 9, we get:
y = (14 +23x9)/17 = 13 <===
inserting y = 13 in equation(1) we get x = 553 <==
Tht is all.

Posted 263 day ago

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jayteacher

For a student with skills limited to math and algebra, I believe the easiest solution to the problem is to make a table with 2 columns. In column 1, S can represent the number of senior citizen members of the sports club, and in column 2, A can represent the number of adult members. To derive an equation with each adult who spent $230 for annual membership and each senior citizen who spent $170 for annual membership and with a total annual income of $129400, mathematically the equation is:
$230A + $170S = $129400.
To represent A as a function of S, A(S) = ($129400 - $170S) / $230, where S = 0, 1, 2 . . . (until A is < or = 0). However, intuitively, we know that A and S must be whole numbers, since a part of a member is meaningless. Therefore, starting at S = 0, S = 1, & S = 2, and then continuing until A is a whole number also, I found that when S = 13 members, A = 553 members.

Posted 266 day ago

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steiner1745

The answer to your problem is 13.
Here is the solution:
Let x be the number of regular members
and y the number of seniors.
Then we must find whole numbers x, y such that
230x + 170 y = 129400
or
23x + 17y = 12940.
This is an example of a Diophantine equation.
Here's how it's solved.
First, note that 12940 = 761*17 + 3,
so we can rewrite the equation as
23x + 17( y-761) = 3.
Let z = y - 761
Then 23x + 17z = 3. (*)
The main idea here will be to maximise x
and minimise z.
Note that
23*3 -17*4 = 1,
so the minimal solution of (*)
is x = 9, z = -12, and any further
solution for x must be of the form 9 + 17k.
Next 23x < 12940 gives us x < 562.
and the maximal value of x is 562-9 = 553.
We find z = -748 and thus y = 13.
Check: 23*553+17*13 = 12940.
Not at all an easy problem for an algebra student!

Posted 267 day ago

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YummyCookies

uhm........u see......ur question is kind of hard for me to understand
because it exactly doesn't ask a question!!!! So pls be more SPECIFIC!!!!!

Posted 267 day ago

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Doctor Bob

Your question without a verb is unclear. I am assuming you ask the difference between the two.

1. (Mathematics) (functioning as singular) a group of related sciences, including algebra, geometry, and calculus, concerned with the study of number, quantity, shape, and space and their interrelationships by using a specialized notation

Collins English Dictionary – Complete and Unabridged 6th Edition 2003. © William Collins Sons & Co. Ltd 1979, 1986 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003

As indicated above, mathematics is a generic word which is inclusive of algebra. CLIFFS QUICK REVIEW OF ALGEBRA introduces Algebra as the branch of mathematics in which letters are used to represent numbers and signs are used to represent operations: a kind of universal arithmetic or simply arithmetic using letters.
Need regular tutoring? RevDrBob@aol.com

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