Three students gambled with the amount of 7: 6: 5 and finished with sums in the ratio 1: 4: 7 . if one of them lost $22, then what would the total amount at the start of the game be?

Make the ratios have a common "total."

7:6:5 is the start
change 1:4:7 to 1.5:6:10.5 so that there are 18 parts.

the only person who lost, lost 5.5 parts which is $22

each part is $4

there are 18 parts, they started out with $72

Hope i can you!