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?

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.