Question

3/4 + ax = 10In the equation above, a is a constant. If x = 24 is the solution to the equation, what is the value of a?

Answer 1

`a\text{ = }(37)/(96)`

Step-by-step explanation

We have the equation:

`(3)/(4)\text{ + ax = 10}`

The solution to the equation is x = 24.

This means that:

`\begin{gathered} (3)/(4)\text{ + a }\cdot\text{ 24 = 10} \\ \text{Collect like terms:} \\ a\cdot\text{ 24 = 10 - }(3)/(4) \\ a\cdot24\text{ = 9}(1)/(4) \\ a\cdot24\text{ = }(37)/(4) \\ \text{Divide through by 24:} \\ a\text{ = }\frac{37}{4\cdot\text{ 24}} \\ a\text{ = }(37)/(96) \end{gathered}`

That is the value of a.