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AQA GCSE · Question 12 · Ratio Proportion and Rates of Change
At a music festival, four types of instrument are played.
<br>
guitars, keyboards, drums, trumpets
<br>
<ul>
<li>The total number of instruments is 80</li>
<li>Half of the instruments are guitars.</li>
<li>keyboards : drums : trumpets = 3 : 4 : 1</li>
</ul>
How many keyboards are there?
At a music festival, four types of instrument are played.
<br>
guitars, keyboards, drums, trumpets
<br>
<ul>
<li>The total number of instruments is 80</li>
<li>Half of the instruments are guitars.</li>
<li>keyboards : drums : trumpets = 3 : 4 : 1</li>
</ul>
How many keyboards are there?
How to approach this question
1. Calculate the number of guitars from the total number of instruments.
2. Subtract the number of guitars from the total to find out how many instruments are left (keyboards, drums, and trumpets combined).
3. Look at the ratio for the remaining instruments. Add up the parts of the ratio to find the total number of parts.
4. Divide the number of remaining instruments by the total number of parts to find the value of one part.
5. Multiply the value of one part by the number of parts for keyboards in the ratio.
Full Answer
**Step 1: Find the number of guitars.**
Half of the instruments are guitars.
Number of guitars = 80 / 2 = 40.
**Step 2: Find the number of remaining instruments.**
These are the keyboards, drums, and trumpets.
Remaining instruments = Total instruments - Number of guitars
Remaining instruments = 80 - 40 = 40.
**Step 3: Use the ratio to find the number of keyboards.**
The ratio for keyboards : drums : trumpets is 3 : 4 : 1.
Total number of parts in the ratio = 3 + 4 + 1 = 8 parts.
These 8 parts represent the 40 remaining instruments.
**Step 4: Find the value of one part.**
Value of one part = Total remaining instruments / Total number of parts
Value of one part = 40 / 8 = 5 instruments.
**Step 5: Calculate the number of keyboards.**
Keyboards have 3 parts in the ratio.
Number of keyboards = 3 parts × 5 instruments per part = 15.
**Answer: 15**
We are given that the total number of instruments is 80.
1. **Guitars:** Half of the instruments are guitars.
Number of guitars = (1/2) * 80 = 40.
2. **Other Instruments:** The rest are keyboards, drums, and trumpets.
Number of other instruments = Total - Guitars = 80 - 40 = 40.
3. **Ratio:** These 40 instruments are shared in the ratio keyboards : drums : trumpets = 3 : 4 : 1.
4. **Total Parts:** Find the total number of parts in the ratio.
Total parts = 3 + 4 + 1 = 8.
5. **Value of One Part:** Divide the number of other instruments by the total parts.
Value of 1 part = 40 / 8 = 5.
6. **Number of Keyboards:** Keyboards correspond to 3 parts in the ratio.
Number of keyboards = 3 * (value of 1 part) = 3 * 5 = 15.
There are 15 keyboards.
Common mistakes
✗ Applying the ratio to the total number of instruments (80) instead of the remaining number (40).
✗ Calculation errors when finding one part of the ratio.
✗ Giving the value of one part (5) as the final answer.
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