There were 350 goldfish and guppies in a shop. 20% of them were goldfish. After some goldfish were added, the percentage of the goldfish increased to 30%. How many goldfish were added
Out of 350 total fish, 20% were goldfish:
0.20 x 350 = 70 goldfish
If the number of goldfish increased enough to make them 30% of the total, then we can set up the equation:
(total number of goldfish + added goldfish) / (total number of fish + added goldfish) = 0.30
Let's use the variable "x" to represent the number of goldfish added.
(70 + x) / (350 + x) = 0.30
To solve for x, we can cross-multiply and simplify:
70 + x = 0.30(350 + x)
70 + x = 105 + 0.30x
0.70x = 35
x = 50
Therefore, 50 goldfish were added to the shop.
Let's solve this step-by-step.
Step 1: Calculate the initial number of goldfish.
If 20% of the total number of fish (350) were goldfish, we can find the initial number of goldfish by multiplying the total number of fish by the percentage:
Initial Number of Goldfish = 20% of 350 = (20/100) * 350 = 70
Step 2: Calculate the initial number of guppies.
The initial number of guppies can be found by subtracting the initial number of goldfish from the total number of fish:
Initial Number of Guppies = Total Number of Fish - Initial Number of Goldfish
Initial Number of Guppies = 350 - 70 = 280
Step 3: Calculate the final number of goldfish.
If the percentage of goldfish increased to 30% after some goldfish were added, we need to find the final number of goldfish. Let's assume x goldfish were added. So, the final number of goldfish is the initial number of goldfish plus the number of goldfish added:
Final Number of Goldfish = Initial Number of Goldfish + Number of Goldfish Added
Final Number of Goldfish = 70 + x
Step 4: Calculate the final total number of fish.
The final total number of fish can be found by adding the final number of goldfish to the initial number of guppies:
Final Total Number of Fish = Final Number of Goldfish + Initial Number of Guppies
Final Total Number of Fish = (70 + x) + 280 = 350 + x
Step 5: Set up an equation using the information given.
The percentage of goldfish after the addition equals 30%, so we can write the equation:
(70 + x) / (350 + x) = 30/100
Step 6: Solve the equation for x.
Cross multiplying the equation, we get:
(70 + x) * 100 = 30 * (350 + x)
7000 + 100x = 10500 + 30x
100x - 30x = 10500 - 7000
70x = 3500
x = 50
Step 7: Find the number of goldfish added.
So, 50 goldfish were added to the shop.