To make a sports drink for the football team, Jaylen filled \dfrac9{10}
10
9
start fraction, 9, divided by, 10, end fraction of a large cooler with water. Then, he filled the remaining space with 666 cups of sports drink concentrate.
How many gallons of sports drink did Jaylen make?
geez -- why not just type 9/10, instead of all that other useless crap?
so 1/10 the volume is 666 cups
That makes the whole thing
6660 cups * 1gal/16cups = 6660/16 gals
But I suspect that 666 is not really what you meant to type, what with your useless copy/paste efforts
To solve this problem, we'll need to follow a few steps:
Step 1: Determine the total volume of the cooler.
Since Jaylen filled $\dfrac{9}{10}$ of the cooler with water, we know that the remaining $\dfrac{1}{10}$ was filled with sports drink concentrate. The ratio of water to concentrate is 9:1. Let's assume the total volume of the cooler is $x$.
Step 2: Calculate the volume of the concentrate.
Since the concentrate fills $\dfrac{1}{10}$ of the cooler, we can find its volume by multiplying the total volume of the cooler by $\dfrac{1}{10}$:
Concentrate volume = $\dfrac{1}{10} \times x = \dfrac{x}{10}$.
Step 3: Convert the concentrate volume to gallons.
Since we're asked for the volume in gallons, we need to convert $\dfrac{x}{10}$ to gallons. Note that 1 gallon is equivalent to 16 cups, so we can use this conversion factor:
Concentrate volume (in gallons) = $\dfrac{x}{10} \times \dfrac{1 \, \text{gallon}}{16 \, \text{cups}}$.
Step 4: Calculate the number of cups of concentrate.
Jaylen added 666 cups of concentrate, so we have the equation:
666 cups = Concentrate volume (in gallons) $\times$ 16 cups/gallon.
Now, let's combine these steps to calculate the answer.
Step 1: Since we don't have the total volume of the cooler, we'll leave it as 'x'.
Step 2: Concentrate volume = $\dfrac{x}{10}$.
Step 3: Concentrate volume (in gallons) = $\dfrac{x}{10} \times \dfrac{1 \, \text{gallon}}{16 \, \text{cups}}$.
Step 4: 666 cups = $\left(\dfrac{x}{10} \times \dfrac{1 \, \text{gallon}}{16 \, \text{cups}}\right) \times 16 \, \text{cups/gallon}$.
Now, we can solve for x:
666 cups = $\dfrac{x}{10}$.
Multiply both sides by 10:
6660 cups = x.
Therefore, Jaylen made a total of 6660 cups of sports drink.
To find out how many gallons of sports drink Jaylen made, we need to calculate the total volume of the drink, including both the water and the sports drink concentrate.
First, let's find the volume of water in the cooler.
The fraction of the cooler filled with water is 9/10.
Since the total volume of the cooler is not given, we can assume any value for it.
For simplicity, let's assume the total volume of the cooler is 10 gallons.
Therefore, the volume of water in the cooler is (9/10) * 10 = 9 gallons.
The remaining space in the cooler is filled with 666 cups of sports drink concentrate.
Since 1 gallon is equal to 16 cups, we can convert the cups into gallons.
666 cups / 16 cups/gallon = 41.625 gallons.
Finally, we can calculate the total volume of the sports drink:
Total volume = volume of water + volume of sports drink concentrate
Total volume = 9 gallons + 41.625 gallons = 50.625 gallons.
Therefore, Jaylen made 50.625 gallons of sports drink.