Question

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$ 3(31-12 t)=82 $$

Short answer

The solution to the equation, when rounded to the nearest hundredth, is \(t = 0.31\).

Step-by-step solution

Simplifying the equation

Firstly, apply distributive property to multiply the 3 into the brackets. The equation then becomes \[3*31 - 3*12t = 82\] which further simplifies to \[93 - 36t = 82\].

Isolating the term with 't'

Next, isolate the term with 't' by moving '93' to the other side of the equation. This can be done by subtracting '93' from both sides, giving \[-36t = 82 - 93\] simplifying to \[-36t = -11\].

Solving for 't'

Now, solve for 't' by dividing both sides of the equation by -36. This gives \(t = \frac{-11}{-36}\).

Rounding to the nearest hundredth

On calculating this division, the answer is approximately 0.30556. However, we're asked to round to the nearest hundredth. Hence, we round the calculated answer to give us \(t = 0.31\).

Checking the solution

Finally, we substitute \(t = 0.31\) back into the original equation to confirm if it is the solution. Substituting, we get \[3(31 - 12 * 0.31) = 82\]. On calculating the left-hand side, it rounds to approximately 82, which is equal to the right-hand side. Hence, the calculated 't' is the correct solution.