There were 350 goldfish and guppies in a shop. 20% of them were goldfish. After some goldfish were added, the percentage of goldfish increased to 30%. How many goldfish were added?
First, we need to figure out how many goldfish and guppies there were originally.
We know that 20% of the total were goldfish, so we can set up an equation:
0.2(Total) = 350
Solving for the total:
Total = 350 / 0.2
Total = 1750
So there were originally 1750 fish in total, and 20% of them were goldfish, which means:
Goldfish = 0.2(1750)
Goldfish = 350
Now we need to figure out how many goldfish were added to increase the percentage to 30%. Let's call the number of goldfish added "x".
We know that the new percentage of goldfish is 30%, so:
(Goldfish + x) / (Total + x) = 0.3
Substituting in what we know:
(350 + x) / (1750 + x) = 0.3
Multiplying both sides by (1750 + x):
350 + x = 0.3(1750 + x)
Distributing on the right side:
350 + x = 525 + 0.3x
Subtracting 0.3x and 350 from both sides:
0.7x = 175
Dividing both sides by 0.7:
x = 250
So 250 goldfish were added to the shop.
Let's solve this step-by-step:
Step 1: Find the number of goldfish initially.
Let's represent the number of goldfish as "G."
According to the problem, 20% of the total number of fish is goldfish, so we can write the equation:
0.20 * (G + 350) = G
Step 2: Simplify and solve the equation for G.
0.20G + 70 = G
0.80G = 70
G = 70 / 0.80
G = 87.5 (approx.)
Since the number of goldfish cannot be a decimal, we can conclude that there were 87 goldfish initially.
Step 3: Find the number of goldfish after some were added.
Let's represent the number of goldfish added as "X."
The equation can be written as:
0.30 * (87 + X + 350) = 87 + X
Step 4: Simplify and solve the equation for X.
0.30X + 163.5 = 87 + X
0.70X = 76.5
X = 76.5 / 0.70
X ≈ 109.29
Since the number of goldfish cannot be a decimal, we can conclude that approximately 109 goldfish were added.
Therefore, approximately 109 goldfish were added.