Answer:
21 questions
Explanation:
Given
![Wrong : Right = 2:7](https://img.qammunity.org/2021/formulas/mathematics/college/qsjk4geqh1u83hyc6yvek7emi4l5ohuuw3.png)
Required
Determine the number of correct answers if he answered 6 wrongly
The required ratio can be represented as:
![Wrong : Right = 6 : X](https://img.qammunity.org/2021/formulas/mathematics/college/bvxjw8p2nd7wqy2l3lb4d15fiht6g9c5j0.png)
Where X represents number of right answers for 6 wrong answers.
Next, we equate both ratios:
![6:X = 2:7](https://img.qammunity.org/2021/formulas/mathematics/college/v8y9bznau4omm52aw6t5fbgjwxqvu4k61z.png)
Convert to fraction
![(6)/(X) = (2)/(7)](https://img.qammunity.org/2021/formulas/mathematics/college/8kawnazz52dadsegyft56aqxav4uo41z2y.png)
Cross Multiply
![X * 2 = 6 * 7](https://img.qammunity.org/2021/formulas/mathematics/college/y2qgnfcbplgfpkkb6goc9bpur2xuer8y8v.png)
![2X = 42](https://img.qammunity.org/2021/formulas/mathematics/college/fh7dsyzbirbk14q0dxlaqof3999g5308hn.png)
Divide through by 2
![X = 21](https://img.qammunity.org/2021/formulas/mathematics/college/3pzvkgmgj5bxcpzz616rn3a9fntov42z4d.png)
Hence, he answered 21 correctly