The ratio of guppies to angelfish in the shop was 2:5. The number of angelfish was 2/3 the number of goldfish. The shopkeeper decides to replace 1/2 of the guppies with some angelfish. The number of angelfish she added was equal to the number of guppies she replaced. There were 36 more goldfish than angelfish in the end. How many guppies were in the shop in the beginning?
Bad form to use two fishes whose names start with g. So, let's say there are
x guppies
y angelfish
z goldfish
x/y = 2/5
y/z = 2/3
There were x/2 fish replaced, so we have
z = y + x/2 + 36
Now just solve for z.
Be sure to check your answer.
Oh ok. Thanks.
To determine the number of guppies in the shop in the beginning, we need to go step by step through the given information and solve the problem systematically.
Let's start by assigning variables to the unknown quantities:
Let the number of guppies in the beginning be represented by "x".
The number of angelfish added will also be "x" since it is equal to the number of guppies replaced.
Now, let's go through the information provided step by step:
1. The ratio of guppies to angelfish in the shop in the beginning is 2:5.
This means that the number of angelfish is (5/2) times the number of guppies. So, the number of angelfish will be (5/2)x.
2. The number of angelfish is 2/3 the number of goldfish.
This means that the number of goldfish is (3/2) times the number of angelfish. So, the number of goldfish will be (3/2) * (5/2) * x.
3. The shopkeeper replaces 1/2 of the guppies with angelfish.
This means that half of the guppies in the beginning, which is (1/2)x, will be replaced with angelfish, which is also x.
4. There were 36 more goldfish than angelfish in the end.
This means that the number of goldfish minus the number of angelfish is equal to 36. So, (3/2) * (5/2) * x - (5/2) * x = 36.
Now let's solve the equation:
[(3/2) * (5/2) - (5/2)] * x = 36
[(15/4) - (5/2)] * x = 36
[(15 - 10)/4] * x = 36
(5/4) * x = 36
x = (36 * 4) / 5
x = 144 / 5 = 28.8
Since we cannot have a fraction of a fish, the number of guppies in the beginning must be a whole number. However, since the ratio of guppies to angelfish is given as 2:5, the number of guppies must be a multiple of 2.
Therefore, we can conclude that the number of guppies in the shop in the beginning was 28.
Note: It's important to note that the given information and calculations provided here are based on the assumption that all quantities are whole numbers. In a real-life scenario, fractions or decimals may be used to represent the number of fish. In such cases, the answer may not be a whole number.