Question

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$ 358=39 c-17 $$

Short answer

The solution for c is approximately 9.62 when rounded to the nearest hundredth.

Step-by-step solution

Isolate the variable term

First, let's move the constant term from the right side of the equation to the left side. To do this, add 17 to both sides of the equation.\[ 358 + 17 = 39c \]This simplifies to:\[ 375 = 39c \]

Solve for the variable

Next, divide both sides of the equation by 39 to get c by itself.\[ c = \frac{375}{39} \]

Round to the nearest hundredth

When you compute the division, you get c approximately equal to 9.62 when rounded to the nearest hundredth.

Check the solution

Let's check the solution by substituting c = 9.62 into the original equation:\[ 358 = 39 \cdot 9.62 - 17 \]Rounding the result of \(39 \cdot 9.62\) to the nearest hundredth and subtracting 17 should yield 358 if our solution is correct.