john has a 25 gallon fish tank. John filled his fish tank today with 24 gallons of water. the water evaporates at a rate of 1.5 gallons per week week. John adds 2 gallons to the tank every other week. At which of the following times will the tank contain 17.5 gallons?
a. exactly 11 weeks from today
b. exactly 14 weeks from today
c. exactly 9 weeks from today
d. exactly 6 weeks from today
And HOW do you get the answer??
do a series, each week.
24, 22.5, 21+2, 21.5, 20+2, 20.5, 19+2, and so on.
Thanks for your help but I still don't get it
I think I got it....11 weeks
To determine at which of the given times the tank will contain 17.5 gallons, we need to consider the rate of water evaporation and the rate at which John adds water.
Given:
Fish tank capacity (maximum volume) = 25 gallons
Amount of water added today = 24 gallons
Rate of water evaporation = 1.5 gallons per week
Rate of water addition every other week = 2 gallons
To find the answer, we can calculate the net change in the water level over time for each option and identify when the tank will contain 17.5 gallons.
Let's examine each option individually:
a. Exactly 11 weeks from today:
- Over 11 weeks, the net change due to evaporation would be 11 * 1.5 = 16.5 gallons. (11 weeks * 1.5 gallons/week)
- Additionally, John would add water 5 times during this period: 2 gallons * (11 weeks / 2 weeks)
- The net change in water level would be 24 gallons - 16.5 gallons + 2 gallons = 9.5 gallons. (amount added - amount evaporated)
- Therefore, the tank would not contain 17.5 gallons after 11 weeks. So, option a is not correct.
b. Exactly 14 weeks from today:
- Over 14 weeks, the net change due to evaporation would be 14 * 1.5 = 21 gallons.
- Additionally, John would add water 7 times during this period: 2 gallons * (14 weeks / 2 weeks)
- The net change in water level would be 24 gallons - 21 gallons + 2 gallons = 5 gallons.
- Therefore, the tank would not contain 17.5 gallons after 14 weeks. So, option b is not correct.
c. Exactly 9 weeks from today:
- Over 9 weeks, the net change due to evaporation would be 9 * 1.5 = 13.5 gallons.
- Additionally, John would add water 4 times during this period: 2 gallons * (9 weeks / 2 weeks)
- The net change in water level would be 24 gallons - 13.5 gallons + 2 gallons = 12.5 gallons.
- Therefore, the tank would not contain 17.5 gallons after 9 weeks. So, option c is not correct.
d. Exactly 6 weeks from today:
- Over 6 weeks, the net change due to evaporation would be 6 * 1.5 = 9 gallons.
- Additionally, John would add water 3 times during this period: 2 gallons * (6 weeks / 2 weeks)
- The net change in water level would be 24 gallons - 9 gallons + 2 gallons = 17 gallons.
- Therefore, the tank would not contain exactly 17.5 gallons after 6 weeks. So, option d is not correct.
Based on the calculations, none of the given options result in exactly 17.5 gallons in the tank.