please help!
Noah knows that his friend Ryan uses 2 small chlorine tablets each week to maintain his 10,000 gallon pool:
1)Write a direct variation equation that relates c and g, where c is the number of chlorine talets and g is pool volume in gallons.
2)How many small chlorine tablets should Noah add each week to is 15,000 gallon pool.
c(g)=2(10,000) and if you want an equivalent, multiply both values by the same number. part b can be solved like (2/10000)=(c/15000), {2(15000)}/10000=c.
1) To write a direct variation equation that relates the number of chlorine tablets (c) and the pool volume in gallons (g), we need to recognize that as the pool volume increases or decreases, the number of chlorine tablets needed will also increase or decrease proportionally.
In a direct variation equation, the ratio between the two variables remains constant. Let's denote this constant ratio as k. In this case, k represents the number of chlorine tablets needed per gallon of pool volume. Therefore, we can write the equation as:
c = k * g
2) To find out how many small chlorine tablets Noah should add each week to his 15,000 gallon pool, we can use the direct variation equation derived in the previous step. However, since we don't know the value of k, we cannot directly substitute it into the equation.
To determine the value of k, we can use the given information: Ryan uses 2 small chlorine tablets for his 10,000 gallon pool. We can set up a proportion to solve for k:
2 tablets / 10,000 gallons = k * g
From this proportion, we can substitute the value of g (15,000 gallons) and solve for k:
2 tablets / 10,000 gallons = k * 15,000 gallons
(2/10,000) = k * 15,000
To isolate k, divide both sides of the equation by 15,000:
(2/10,000) / 15,000 = k
This will give us the value of k (the constant ratio), which we can then substitute into the direct variation equation:
c = k * g
c = (2/10,000) * 15,000
Now, we can calculate the value of c:
c = (2/10,000) * 15,000
c = 3 tablets
Therefore, Noah should add 3 small chlorine tablets each week to his 15,000 gallon pool.