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09 Jun 2026, 22:05
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E
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Difficulty:
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Question Stats:
47% (03:20) correct
53%
(03:21)
wrong
based on 62
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In Burenville, each full-time teacher earns three times as much as each part-time teacher. The city will lay off 5% of its full-time teachers and 10% of its part-time teachers and thereby reduce its teacher payroll by 9%.
What fraction of the teachers that will be laid off are part-time teachers?
(A)\(\frac{8}{11}\)
(B)\(\frac{6}{7}\)
(C)\(\frac{8}{9}\)
(D)\(\frac{12}{13}\)
(E)\(\frac{24}{25}\)
What fraction of the teachers that will be laid off are part-time teachers?
(A)\(\frac{8}{11}\)
(B)\(\frac{6}{7}\)
(C)\(\frac{8}{9}\)
(D)\(\frac{12}{13}\)
(E)\(\frac{24}{25}\)
11 Jun 2026, 02:16
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Solution will be posted in a couple of hours
11 Jun 2026, 07:36
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We are told that a full-time teacher earns three times as much as a part-time teacher , so let’s assume that their earnings are 3 and 1 respectively.
Suppose that there are f full time and p part time teachers . The total teacher payroll is 3f + p
0.1p part time and 0.05f full time teachers will be laid off
The savings in teacher payroll will be 0.05(3)(f) + 0.1(1)p, and this is 9% of 3f + p
Thus 0.15f +0.1p = 0.27f + 0.09p
We see that p = 12f
We want to know what fraction 0.1p is of 0.1p + 0.05f
This is equal to 10p divided by (10p + 5f)
(I multiplied both by 100)
As p= 12f, the required fraction is 120f /125f = 24/25
Suppose that there are f full time and p part time teachers . The total teacher payroll is 3f + p
0.1p part time and 0.05f full time teachers will be laid off
The savings in teacher payroll will be 0.05(3)(f) + 0.1(1)p, and this is 9% of 3f + p
Thus 0.15f +0.1p = 0.27f + 0.09p
We see that p = 12f
We want to know what fraction 0.1p is of 0.1p + 0.05f
This is equal to 10p divided by (10p + 5f)
(I multiplied both by 100)
As p= 12f, the required fraction is 120f /125f = 24/25
14 Jun 2026, 10:04
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num of full time = x
num of part time = y
salary for each full time = 3p
salary for each part time = p
total payroll = 3px + py
now 5% of full time laid off.
laid off= 5x/100
so left FT = 95x/100
10% of PT laid off.
laid off = 10y/100
so left PT = 90y/100
new pay roll is 91% of actual payroll.
(95x/100) 3P + (90y/100)P = 91/100 (3xp + py)
upon solving this, we get
X = y/12
we need to find 10y/ 5x+10y
upon placing value of X and solving this,
we get 24/25
option E
num of part time = y
salary for each full time = 3p
salary for each part time = p
total payroll = 3px + py
now 5% of full time laid off.
laid off= 5x/100
so left FT = 95x/100
10% of PT laid off.
laid off = 10y/100
so left PT = 90y/100
new pay roll is 91% of actual payroll.
(95x/100) 3P + (90y/100)P = 91/100 (3xp + py)
upon solving this, we get
X = y/12
we need to find 10y/ 5x+10y
upon placing value of X and solving this,
we get 24/25
option E
kevincan
