Answer :
Sure, let's go through the problem step by step and find the answers.
### Part A:
1. Tom has a water tank that holds 5 gallons of water.
2. He uses water from a full tank to fill 6 bottles that each hold 16 ounces and a pitcher that holds [tex]\(\frac{1}{2}\)[/tex] gallon.
3. We need to find out how many ounces of water are left in the water tank.
First, let's convert everything to the same unit, which is ounces.
- 1 gallon = 128 ounces
Therefore, Tom's tank capacity in ounces:
[tex]\[
5 \text{ gallons} \times 128 \text{ ounces/gallon} = 640 \text{ ounces}
\][/tex]
- 6 bottles, each holding 16 ounces:
[tex]\[
6 \times 16 \text{ ounces} = 96 \text{ ounces}
\][/tex]
- 1 pitcher holding [tex]\(\frac{1}{2}\)[/tex] gallon:
[tex]\[
\frac{1}{2} \text{ gallon} \times 128 \text{ ounces/gallon} = 64 \text{ ounces}
\][/tex]
- Total water used:
[tex]\[
96 \text{ ounces} (from bottles) + 64 \text{ ounces} (from pitcher) = 160 \text{ ounces}
\][/tex]
- Water left in the tank:
[tex]\[
640 \text{ ounces} (total) - 160 \text{ ounces} (used) = 480 \text{ ounces}
\][/tex]
So, Tom has 480 ounces of water left in the tank.
### Part B:
1. Tom drinks 4 pints of water a day.
2. We need to find out how many full tanks of water he will drink in 30 days.
First, let's convert everything to the same unit. This time, let's convert pints to gallons and then find out how it relates to the tank's capacity.
- 1 pint = 0.125 gallons
[tex]\[
4 \text{ pints/day} \times 0.125 \text{ gallons/pint} = 0.5 \text{ gallons/day}
\][/tex]
- Total water intake in 30 days:
[tex]\[
0.5 \text{ gallons/day} \times 30 \text{ days} = 15 \text{ gallons}
\][/tex]
- Number of full tanks in 30 days:
[tex]\[
\frac{15 \text{ gallons}}{5 \text{ gallons/tank}} = 3 \text{ tanks}
\][/tex]
So, Tom will drink 3 full tanks of water in 30 days.
### Part A:
1. Tom has a water tank that holds 5 gallons of water.
2. He uses water from a full tank to fill 6 bottles that each hold 16 ounces and a pitcher that holds [tex]\(\frac{1}{2}\)[/tex] gallon.
3. We need to find out how many ounces of water are left in the water tank.
First, let's convert everything to the same unit, which is ounces.
- 1 gallon = 128 ounces
Therefore, Tom's tank capacity in ounces:
[tex]\[
5 \text{ gallons} \times 128 \text{ ounces/gallon} = 640 \text{ ounces}
\][/tex]
- 6 bottles, each holding 16 ounces:
[tex]\[
6 \times 16 \text{ ounces} = 96 \text{ ounces}
\][/tex]
- 1 pitcher holding [tex]\(\frac{1}{2}\)[/tex] gallon:
[tex]\[
\frac{1}{2} \text{ gallon} \times 128 \text{ ounces/gallon} = 64 \text{ ounces}
\][/tex]
- Total water used:
[tex]\[
96 \text{ ounces} (from bottles) + 64 \text{ ounces} (from pitcher) = 160 \text{ ounces}
\][/tex]
- Water left in the tank:
[tex]\[
640 \text{ ounces} (total) - 160 \text{ ounces} (used) = 480 \text{ ounces}
\][/tex]
So, Tom has 480 ounces of water left in the tank.
### Part B:
1. Tom drinks 4 pints of water a day.
2. We need to find out how many full tanks of water he will drink in 30 days.
First, let's convert everything to the same unit. This time, let's convert pints to gallons and then find out how it relates to the tank's capacity.
- 1 pint = 0.125 gallons
[tex]\[
4 \text{ pints/day} \times 0.125 \text{ gallons/pint} = 0.5 \text{ gallons/day}
\][/tex]
- Total water intake in 30 days:
[tex]\[
0.5 \text{ gallons/day} \times 30 \text{ days} = 15 \text{ gallons}
\][/tex]
- Number of full tanks in 30 days:
[tex]\[
\frac{15 \text{ gallons}}{5 \text{ gallons/tank}} = 3 \text{ tanks}
\][/tex]
So, Tom will drink 3 full tanks of water in 30 days.
