James, Karen, and Lou are hiking. Lou forgot to bring any water. James brought 2 gallons of water and Karen brought 1 and 3/4 gallons of water. The three of them agree to divide all the water equally among them. Lou gives $2 for the water he receives, which James and Karen agree to divide fairly between the two of them. How much money should James receive?

Question

James, Karen, and Lou are hiking. Lou forgot to bring any water. James brought 2 gallons of water and Karen brought 1 and 3/4 gallons of water. The three of them agree to divide all the water equally among them. Lou gives $2 for the water he receives, which James and Karen agree to divide fairly between the two of them. How much money should James receive?

Answer 1

To answer this question, let's break it down step by step:

Step 1: Calculate the total amount of water they have.
James has 2 gallons, and Karen has 1 and 3/4 gallons. To find the total, we need to add these two amounts.

2 gallons + 1 and 3/4 gallons = 3 and 3/4 gallons

So, they have a total of 3 and 3/4 gallons of water.

Step 2: Calculate the amount of water each person will get.
Since they agreed to divide the water equally among them, we need to find out the share of each person.

To do this, we divide the total amount of water by the number of people.

3 and 3/4 gallons ÷ 3 people = 1 and 1/4 gallons

Each person will get 1 and 1/4 gallons of water.

Step 3: Calculate the amount of money Lou gave.
Since Lou gave $2 for the water, we now need to find out the value of $1 and 1/4 gallons of water.

To do this, we divide the amount Lou gave by the water he received.

$2 ÷ 1 and 1/4 gallons = $1.60 (rounded to two decimal places)

So, the value of $1 and 1/4 gallons of water is $1.60.

Step 4: Calculate the fair share of money for James and Karen.
Since Lou gave $2, which James and Karen agreed to divide fairly between them, we need to divide this amount equally between the two of them.

To do this, we divide the amount by 2.

$2 ÷ 2 = $1

So, each of them should receive $1.

Therefore, James should receive $1.

Answer 2

How much do they have?

2 + 1 3/4 = 3 3/4 = 15/4

each gets (15/4)/3 = 5/4

James put in 2/(15/4) of the total
=8/15

Karen put in (7/4)/(15/4) = 7/15 of total

James (8/15) * $ 2 = $ 1.07

Karen (7/15) * $ 2 = $ 0.93

Answer 3

2 + 1 3/4 = 3 3/4 = 15/4

each gets (15/4)/3 = 5/4

James put in 2/(15/4) of the total
=8/15

Karen put in (7/4)/(15/4) = 7/15 of total

James (8/15) * $ 2 = $ 1.07

Karen (7/15) * $ 2 = $ 0.93