The ratio of guppies to angelfish in a shop was 2:3. The number of angelfish was 2/3 the number of gold fish. The shoe keeper decided to replace 1/4 of the guppies with some angelfish. The number of angelfish she added was equal to the number of the guppies she replaced. There were 30 more guppies were in the shop in the beginning?
list the facts:
g/a = 2/3
a = 2/3 f
The shop keeper decided to replace 1/4 of the guppies with some angelfish. The number of angelfish she added was equal to the number of the guppies she replaced.
well, duh. Both sentences say the same thing.
The last sentence leaves us dangling, as well as being incomprehensible.
10
Uh the answer is 48 for how many angelfish there are and the other answer is 36 for goldfish.
60 guppies
60 guppies in the beginning
if u set "portion per fish" as x
then the equation would be
3x / 2/3 - (2x * 1/4 + 3x) = 30
4.5x - 3.5x = 30
x = 30
since the beginning, guppies was 2 portions while angelfish was 3....
there was 60 guppies in the beginning and 90 angelfish. if u don't believe me then solve it backwards
To solve this problem, let's break it down into steps:
Step 1: Assign variables and set up equations:
Let's assume the number of guppies initially in the shop is represented by "2x", and the number of angelfish is represented by "3x".
According to the information given, the number of angelfish is 2/3 the number of goldfish, so the number of goldfish can be represented by "(3x * 2/3)" or simply "2x".
Step 2: Calculate the number of guppies and angelfish added/replaced:
The shoekeeper decided to replace 1/4 of the guppies. Since there were initially 2x guppies in the shop, the number of guppies replaced is (1/4) * 2x = x/2.
To maintain the same number of angelfish as the guppies replaced, the number of angelfish added must also be x/2.
Step 3: Update the number of guppies and angelfish in the shop:
After replacing 1/4 of the guppies, we subtract x/2 from the initial number of guppies:
New number of guppies = 2x - x/2 = (4x - x)/2 = 3x/2
The number of angelfish remains constant at 3x.
Step 4: Set up an equation to solve for x:
According to the problem, there are 30 more guppies in the shop initially than after the replacement. Therefore, we can set up an equation: 3x/2 + 30 = 2x.
Step 5: Solve for x:
Let's solve the equation:
3x/2 + 30 = 2x
Multiply both sides by 2 to eliminate the fraction:
3x + 60 = 4x
Subtract 3x from both sides:
60 = x
Step 6: Calculate the initial number of guppies:
The initial number of guppies is 2x, where x = 60:
Initial number of guppies = 2 * 60 = 120.
Therefore, there were initially 120 guppies in the shop.