Math worksheet with fish and aquarium-themed word problems for students to solve.

Let's solve each problem step by step.

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Problem 1:

Tyger Salamander is going to buy some Clown Fish which cost £12 each and some Angel Fish which cost £7 each. He spends exactly £100 on fish. How many of each fish did he buy?

We need to find two numbers (let’s call them $ x $ and $ y $) such that:
- $ 12x + 7y = 100 $
- $ x $ and $ y $ are whole numbers (you can't buy a fraction of a fish)

Let’s try different values of $ x $ (number of Clown Fish) and see if $ y $ comes out as a whole number.

We can rearrange the equation:
$$
7y = 100 - 12x \Rightarrow y = \frac{100 - 12x}{7}
$$

Now test integer values of $ x $:

| $ x $ | $ 12x $ | $ 100 - 12x $ | $ y = (100 - 12x)/7 $ |
|--------|----------|------------------|-------------------------|
| 0 | 0 | 100 | 100/7 ≈ 14.28 → no |
| 1 | 12 | 88 | 88/7 ≈ 12.57 → no |
| 2 | 24 | 76 | 76/7 ≈ 10.86 → no |
| 3 | 36 | 64 | 64/7 ≈ 9.14 → no |
| 4 | 48 | 52 | 52/7 ≈ 7.43 → no |
| 5 | 60 | 40 | 40/7 ≈ 5.71 → no |
| 6 | 72 | 28 | 28/7 = 4 → ✔ YES! |
| 7 | 84 | 16 | 16/7 ≈ 2.29 → no |
| 8 | 96 | 4 | 4/7 ≈ 0.57 → no |

Only when $ x = 6 $, we get $ y = 4 $

So:
- Clown Fish: 6 × £12 = £72
- Angel Fish: 4 × £7 = £28
- Total: £72 + £28 = £100 ✔

✔ Answer: Tyger bought 6 Clown Fish and 4 Angel Fish.

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Problem 2:

Tyger bought 4 accessories for his aquarium. He spent exactly £80. Which item didn’t he choose?

List of items and prices:
- Treasure Chest: £16
- Pirate Ship: £35
- Large Plastic Skull: £22
- Aquarium Plant: £17
- Gravel: £12

He chose 4 of these 5 items and spent £80.

So, the item not chosen must be the one whose price makes the total of the other four equal to £80.

Let’s compute the total cost of all 5 items:
$$
16 + 35 + 22 + 17 + 12 = 102
$$

If he didn’t buy one item, then:
$$
\text{Sum of 4 items} = 102 - \text{price of missing item} = 80
$$

So:
$$
102 - x = 80 \Rightarrow x = 102 - 80 = 22
$$

So the missing item costs £22 → Large Plastic Skull

✔ Answer: Tyger didn’t choose the Large Plastic Skull.

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✔ Final Answers:

1) 6 Clown Fish and 4 Angel Fish
2) Large Plastic Skull (the item he didn’t choose)