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?
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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.
.
