马上考试~求助一道prep数学题 settled

Suppose the number of manager is 1, and the number of director is n, if we can caculate n, surely we can find the percentage of directors
for (1): S(m) + n* S(d) = (S(m) + 5000)*(1+n);
for (2): S(m) + n * S(d) = (S(d)  - 15000) *(1+n);

==> S(d) - S(m) = 20000;  and S(m) + n*S(d) = S(m) + nS(m) + 5000 + 5000n
==> n(S(d)-S(m)) = 5000 + 5000n ==> 20000n = 5000 + 5000n ==> n = 1/3

So the percent of Directors is n/1+n , (1)+(2) is sufficient.

我这道题当时的时候也不会

Suppose the number of manager is 1, and the number of director is n, if we can caculate n, surely we can find the percentage of directors
for (1): S(m) + n* S(d) = (S(m) + 5000)*(1+n);
for (2): S(m) + n * S(d) = (S(d)  - 15000) *(1+n);

==> S(d) - S(m) = 20000;  and S(m) + n*S(d) = S(m) + nS(m) + 5000 + 5000n
==> n(S(d)-S(m)) = 5000 + 5000n ==> 20000n = 5000 + 5000n ==> n = 1/3

So the percent of Directors is n/1+n , (1)+(2) is sufficient.

for (1), replace x ==> 12u = 8y + 12 ==> 3*4*u = 4*2*y+ 3*4, we can only sure 3 is a factor is y but can't sure 2 or 2*2 is also a factor of y. LCD not sure.
for (2), replace y ==> x = 8*3*4*z + 3*4= (3*4)(8z+1), as x must be divided by 3*4, we can sure know the LCD is 3*4. because y already includes 3*4 as a factor.