Mr. Jones has to mix a fertilizer solution for his garden. The instructions on the package say to dissolve three-fourths of a cup of fertilizer in 5 gallons of water. He has a 40-gallon tank that he pulls with a yard tractor. He only puts 25 gallons of water in the tank each time. How many cups of fertilizer does he need to add to the tank before filling it with water?
If he only puts 25 gallons of water in the tank each time, he needs to adjust the amount of fertilizer accordingly.
First, let's find out the ratio of fertilizer to water in the recommended solution:
3/4 cup fertilizer : 5 gallons water
To make 1 gallon of this solution, we need to divide both parts by 5:
3/4 cup fertilizer ÷ 5 = 0.15 cup fertilizer
5 gallons water ÷ 5 = 1 gallon water
So the ratio is:
0.15 cup fertilizer : 1 gallon water
To make 25 gallons of this solution, we need to multiply both parts by 25:
0.15 cup fertilizer x 25 = 3.75 cups fertilizer
1 gallon water x 25 = 25 gallons water
So Mr. Jones needs to add 3.75 cups of fertilizer to the tank before filling it with water.
To find out how many cups of fertilizer Mr. Jones needs to add to the tank, we need to calculate the ratio of cups of fertilizer to gallons of water mentioned in the instructions.
According to the package instructions, 3/4 (three-fourths) of a cup of fertilizer needs to be dissolved in 5 gallons of water. Therefore, the ratio is:
(3/4 cup) : (5 gallons)
We can simplify this ratio by multiplying both sides by 4 to get whole numbers:
(3/4) * 4 cups : 5 * 4 gallons
This becomes:
3 cups : 20 gallons
Now, since Mr. Jones only puts 25 gallons of water in the tank each time, we can determine the cups of fertilizer needed using proportions:
3 cups -> 20 gallons
x cups -> 25 gallons
Using the property of proportions, we cross-multiply to solve for x:
3 * 25 = 20 * x
75 = 20x
Now, divide both sides of the equation by 20 to isolate x:
75 / 20 = x
x = 3.75 cups
Therefore, Mr. Jones needs to add 3.75 cups of fertilizer to the tank before filling it with water.