Gerald uses (1/5)L of a syrup and some water to make a drink. The amount of water he uses is 3 times the amount of syrup. He then pours the drink into bottles of (1/5)L each. How many bottles of the drink does Gerald have?
so, he uses 1/5 L of syrup
and 3 times that much, or 3/5 L of water.
1/5 + 3/5 = 4/5, so 4 bottles of 1/5 L each.
Let's start by finding the amount of water Gerald uses. We are given that the amount of water is 3 times the amount of syrup.
Let's say Gerald uses x liters of syrup. Then the amount of water he uses would be 3 * x liters.
Now, let's find the total amount of liquid in the drink. The drink is made up of the syrup and the water, which adds up to (1/5)L + 3x.
Next, we need to determine how many bottles Gerald has. Each bottle has a capacity of (1/5)L.
To find the number of bottles, we need to divide the total amount of liquid by the capacity of each bottle.
So, the number of bottles Gerald has is (1/5)L + 3x / (1/5)L.
To simplify, we can multiply the numerator and denominator of the second fraction by 5 to get:
(5 * (1/5)L + 5 * 3x) / (1/5)L
Simplifying further, we have:
(1L + 15x) / (1/5)L
Dividing by a fraction is equivalent to multiplying by its reciprocal:
(1L + 15x) * (5L/1) = 5L + 75x
Therefore, Gerald has 5L + 75x bottles of the drink.
To find out how many bottles of the drink Gerald has, we need to determine the total volume of the drink he made.
Let's start by assigning variables to the unknowns. Let's say Gerald used x liters of syrup.
According to the problem, the amount of water Gerald uses is 3 times the amount of syrup. Therefore, the amount of water he used is 3x liters.
The total volume of the drink is the sum of the amount of syrup and the amount of water. So, the total volume is x liters + 3x liters, which simplifies to 4x liters.
Now, we know that Gerald pours this total volume into bottles of (1/5)L each. The total volume is 4x liters, and each bottle has a volume of (1/5)L, which is equivalent to 4x/5 liters.
To find out how many bottles Gerald has, we need to divide the total volume of the drink by the volume of each bottle.
So, the number of bottles Gerald has is given by the equation:
Number of bottles = Total volume of the drink / Volume of each bottle
Number of bottles = (4x liters) / (4x/5 liters per bottle)
Number of bottles = 4x * (5 / 4x)
Number of bottles = 5
Therefore, Gerald has 5 bottles of the drink.