Zack watered his garden with 1 3/8 gallons of water the first week he planted it. He watered it with 1 3/4 gallons the second week, and 2 1/8 gallons the third week. If he continued watering in this pattern, how much water did he use on the fifth week?
To determine how much water Zack used on the fifth week, we need to continue the given pattern. Let's break it down:
First week: 1 3/8 gallons
Second week: 1 3/4 gallons
Third week: 2 1/8 gallons
To find out how much water Zack used on the fourth week, we can calculate the pattern's difference. Subtract the amount of water used in the first week from the second week:
1 3/4 gallons - 1 3/8 gallons = (4/4 + 3/4) gallons - (3/4 + 1/8) gallons
= 7/4 gallons - 7/8 gallons
= 14/8 - 7/8 gallons
= 7/8 gallons
So, Zack used 7/8 of a gallon of water in the fourth week.
Now, to determine how much water Zack used on the fifth week, we need to continue the pattern:
Fourth week: 7/8 gallons
Fifth week: (7/8 gallons) + (7/8 gallons) = 14/8 gallons
Therefore, Zack used 14/8 gallons, or 1 3/4 gallons, of water on the fifth week.