The first question is simple. I am in the sixth grade, that is, 450÷( 1+50%)=300 yuan is equal to the original price, because 450 divided by its corresponding score is a unit, which is the cost price. Then 20% discount for 450, 450×0.8=360 yuan, this is the selling price, and 360-300=60 yuan.

The second question is beyond my understanding, and this is the answer I found online:

Take point h on AC so that AH=MN.

AM divides ∠BAC equally, so MH=MN

BM+MN=BM+MH

In order to minimize BM+MN=BM+MH, BM+MN=BM+MH=BH if and only if the straight lines H, M, B*** and BH are perpendicular to AC.

At this time △ABH is an isosceles right triangle.

BH= (radical number 2)/2 AB= (radical number 2)/2 * 4 Radical number 2=4

or

Take m as the fixed point first, and then when MN is the smallest, MN⊥AB.

Jean ME⊥AC

∵AD is the bisector of∝∠ ∝∠BAC.

∴ME=MN

In △BME, if BM+ME is the smallest, then B, M and E are on the same straight line.

∴BE⊥AC

∫∠BAC = 45 AB = 4∠2。

∴BE=4, that is, the minimum value of BM+MN is 4.

Because it is.