1. a tank is half full of water. when 9 gallons are added, the tank is 7/8 full. what is the capacity of the tank in gallons?

Tank is half full of water meaning = 0.5
when 9 gallons are added = 0.875 total amount of water in tank

what is 9 gallons = 0.875 - 0.5 = 0.375
9 GALLONS = 0.375 OF TANK

WHAT WILL BE GALLONS IF WHOLE TANK IS COMPLETELY FULL = 1 OF TANK

SO TO CALCULATE LET US TAKE VALUE OF UNKNOWN GALLONS AS X :

9 gallons = 0.375
X gallons = 1
CROSS MULTIPLY : X × 0.375 = 9 × 1
X = 9 / 0.375 = 24 gallons

OR , second method

let us say tank consists of 8 parts
so half water in tank = 4 / 8
we know that 9 gallons + half of tank = 7 / 8

so 9 gallons = 7 / 8 - 4 / 8 = 3 / 8

if 9 gallons = 3 / 8
what gallons in = 8 / 8 ( meaning whole 1 tank )

so 8 / 8 = 1

X gallons = 1 × 9 / (3 / 8 )
X = 9 / (3 / 8 ) = 9 / 0.375 = 24 GALLONS

TOOK A LONG TIME TO WRITE AND I HOPE IT HELPED YOU !!!