Question

At the start of the month a shop had 20-inches and 40-inches television sets in the ratio 4:5. By the end of the month, 200 20-inches and 500 40-inches were sold and the ratio of 20-inches to 40-inches television sets became 1:1. How many television sets of each type were there at the start of the month?

Answer 1

58 tv sets of each type

Answer 2

Hmmmm
intersting

reatio is 4:5
after 200 of the left side was sold and 500 of the right side was sold, then they are equal

so say x=y
x is right side
y is left side
when they are equal ( at end) x=y

x+200=starting number of 20 inch
y+500=starging number of 40 inch
that is in rati 4:5
so

(x+200)/(y+500)=4/5
x=y
(x+200)/(x+500)=4/5
cross multiply aka times both sides by 5(x+500)
5(x+200=4(x+500)
expand
5x+1000=4x+2000
minus 4x both sides
x+1000=2000
minus 1000 both sides
x=1000
y=1000

startx=x+200=1000+200=1200
starty=y+500=1000+500=1500



there are 1200  of the 20-inch TV sets and 1500 of the 40-inch TV sets