At an electronics store, the number of 37 inch hdtvs that is expected to be sold in a month is double that of 58 inch hdtvs and 50 inch hdtvs combined. sales of 58 inch and 50 inch hdtvs are expected to be equal. 58 inch hdtvs sell for 4800 50 inch hdtvs sell for 2000 and 37 inch hdtvs sell for 1800. if the total sales of $168000 are expected this month how many of each hdtvs should be stocked

Will represent as such
number of 37 inch tvs=x
number of 58 inch tvs=y
number of 50 inch tvs =z

x is double of (y+z)
x=2(y+z)
y=z
therefor
x=2(y+y)=2(z+z)=4y=4z
x=4y=4z
y=$4800
z=$2000
x=$1800

4800y+2000z+1800x=168000
undistribute the 100
100(48y+20z+18x)=100(1680)
divide the whole thing by 100
48y+20z+18x=1680
divide the whole thing by 2
24y+10z+9x=840
y=z
24y+10z=34y or 34z
34y+9x=840
convert 9x to y by multiply 4
9x times 4=36y or 36z
34y+36y=840
70y=840
divide both sides by 70
y=12
y=z
z=12
x=4z
x=4(12)
x=48

they should stock:
12      50 inch tvs
12      58 inch tvs
48      38 inch tvs

Logical equivalent of the give question is its contrapositive