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A zoo counts its animals - OCR - GCSE Maths - Question 10 - 2023 - Paper 5
Question 10
A zoo counts its animals. The ratio of antelope to zebra is 3 : 2. The ratio of meerkats to zebra is 7 : 3. (a) Write the number of antelope as a percentage of the ... show full transcript
Worked Solution & Example Answer:A zoo counts its animals - OCR - GCSE Maths - Question 10 - 2023 - Paper 5
Step 1
(a) Write the number of antelope as a percentage of the number of zebra.
Answer
To find the percentage of antelope in relation to zebra, we first establish the ratios provided:
- The ratio of antelope to zebra is 3:2.
- This means, assuming the number of zebra is 2x, the number of antelope would be 3x.
To express the number of antelope as a percentage of zebra, we use the formula:
Substituting the values we have:
Step 2
(b) There are 15 more meerkats than antelope.
Answer
Let the number of antelope be represented as A and meerkats as M.
From the previous part, we know:
- A = 3x
- M = 7/3 of the number of zebra, which is 7/3 * (2x) = \frac{14x}{3}.
According to the information given, the relationship between meerkats and antelope can be expressed as:
Substituting for A and M gives:
To eliminate the fraction, we multiply every term by 3:
Rearranging:
This simplifies to:
Now substituting back to find the number of zebra:
The number of zebra (Z) can be found as:
Thus, the number of zebra in the zoo is 18.