A broken faucet leaks one gallon every 1.33 months. the amount of months that pass,m, varies directly with the amount of gallons that are leaked, g. find the equation that models this variation. How many months will it take for the faucet to leak 7 gallons of water
To find the equation that models this variation, we can use the formula for direct variation: y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of variation.
In this case, the dependent variable is the amount of months that pass, m, and the independent variable is the amount of gallons that are leaked, g. So, our equation will be m = kg.
We are given that the faucet leaks one gallon every 1.33 months. So, when g = 1, m = 1.33. Substituting these values into our equation, we get 1.33 = 1k, which means k = 1.33.
Therefore, the equation that models this variation is m = 1.33g.
To find how many months it will take for the faucet to leak 7 gallons of water, we substitute g = 7 into our equation:
m = 1.33(7)
m = 9.31
It will take 9.31 months for the faucet to leak 7 gallons of water.
To find the equation that models the variation, we can use the direct variation formula:
m = k * g
Where:
m represents the number of months,
g represents the number of gallons leaked, and
k is the constant of variation.
Given that the faucet leaks one gallon every 1.33 months, we can substitute the values to find the constant of variation:
1.33 = k * 1
k = 1.33
Therefore, the equation that models this variation is:
m = 1.33 * g
To find how many months it will take for the faucet to leak 7 gallons of water, we can substitute the value of g = 7 into the equation:
m = 1.33 * 7
m = 9.31
Therefore, it will take approximately 9.31 months for the faucet to leak 7 gallons of water.
To find the equation that models this variation, we first need to identify the constant of variation. In this case, we are told that the amount of months, m, varies directly with the amount of gallons that are leaked, g.
We can set up a proportion with the amount of months, m, and the amount of gallons, g:
m/g = k
Where k is the constant of variation.
Given that the broken faucet leaks one gallon every 1.33 months, we can substitute these values into the equation:
1.33/1 = k
Simplifying this equation gives us k = 1.33.
Now, we have the equation for this variation:
m = 1.33g
To find how many months it will take for the faucet to leak 7 gallons of water, we substitute the value of g = 7 into the equation:
m = 1.33(7)
m = 9.31
Therefore, it will take approximately 9.31 months for the faucet to leak 7 gallons of water.