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In Linguistics 101, the ratio of the number of juniors to the number of seniors is 3:2.  When six more juniors join the class, and one senior drops the class, the ratio of the number of juniors to the number of seniors becomes 2:3.  How many students are in the class after these changes?

Jul 1, 2023

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In Linguistics 101, the ratio of the number of juniors to the number of seniors is 3:2.  When six more juniors join the class, and one senior drops the class, the ratio of the number of juniors to the number of seniors becomes 2:3.  How many students are in the class after these changes?

I can tell you immediately that increasing the number

of juniors will not invert the ratio.  But I'll go through

the motions for you anyway.

J          3

––   =   ––

S          2

J + 6          2

––––   =   –––

S – 1          3

Cross multiply both                            2J  =  3S            (eq 1)

3J + 18  =  2S – 2      (eq 2)

Get either J or S in terms of the

other.  It doesn't matter which,

but J would be simpler.                       J  =  3S/2

Substitute this in eq 2                (3) • (3S/2) + 18  =  2S – 2

9S/2 + 18  =  2S – 2

Multiply both sides by 2                      9S + 36  =  4S – 4

Subtract 4S from both sides               5S + 36  =  –4

Subtract 36 from both sides                    5S  =  –40

You cannot have a negative number of seniors

so something is wrong somewhere.  The error

is in the initial proposition.  This problem has ...... no solution.

.

Jul 7, 2023