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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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Chapter
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BuyFindarrow_forward

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Donations The Enormous State University Good Works Society recently raised funds for three worthwhile causes: the Math Professors' Benevolent Fund (MPBF), the Society of Computer Nerds (SCN), and the NY Jets. Because the society's members are closet jocks, the society donated twice as much to the NY Jets as to the MPBF, and it donated equal amounts to the first two funds. (It is unable to distinguish between mathematicians and nerds.) Further, for every $1 it gave to the MPBF, it decided to keep $1 for itself; for every $1 it gave to the SCN, it kept $2; and for every $1 to the Jets, it also kept $2. The treasurer of the Society, Johnny Treasure, was required to itemize all donations for the Dean of Students but discovered to his consternation that he had lost the receipts! The only information available to him was that the society's bank account had swelled by $4,200. How much did the society donate to each cause?

To determine

To calculate: The funds raised for each cause. The society donated twice as much to the NY Jets as to the MPBF and equal amounts to MPBF and SCN. For each $1 to MPBF society kept $1 to itself and for SCN and NY jets for every dollar, they kept $2 for itself. The total amount in societies bank is $4200.

Explanation

Given Information:

The society donated twice as much to the NY Jets as to the MPBF and equal amounts to MPBF and SCN. For each $1 to MPBF society kept $1 to itself and for SCN and NY jets for every dollar, they kept $2 for itself. The total amount in societies bank is $4200.

Formula Used:

Elimination method:

In this method, we first combine the equations in a way such that one of the variables gets eliminated. Then we substitute this obtained value in either of the equation to get the value of the other variable.

Calculation:

Let the funds raised for MPBF, SCN and NY jets be x,y,z respectively.

The amount of money donated to the NY Jets was equal to twice the amount of money donated to the MPBF.

Thus, we can say that:

z=2x …… (1)

The society donated equal amounts to the first two funds.

Thus,

x=y …… (2)

Also, for each $1 to MPBF society kept $1 to itself and for SCN and NY jets for every dollar they kept $2 for itself and the total amount in societies bank is $4200. This can be referred to as

x+2y+2z=4200 …… (3)

Apply the elimination method to find the solution of the given system of the equations:

Put values of y and z from the first and second equation in third

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