Question

1. find the width of the rectangular prism when the surface area is 208 square centimeters.
2. the amount of money in your savings account after m months is

Explanation:

Step1: Recall surface - area formula

The surface - area formula for a rectangular prism is $S = 2(lw+lh + wh)$, where $l = 6$ cm, $h = 8$ cm, and $S=208$ square cm. Substitute the values into the formula: $208=2(6w + 6\times8+w\times8)$.

Step2: Simplify the equation

First, divide both sides of the equation by 2: $\frac{208}{2}=\frac{2(6w + 48+8w)}{2}$, which gives $104=6w + 48+8w$.

Step3: Combine like - terms

Combine the $w$ terms: $104=(6w + 8w)+48$, so $104 = 14w+48$.

Step4: Isolate the variable term

Subtract 48 from both sides: $104 - 48=14w+48 - 48$, resulting in $56 = 14w$.

Step5: Solve for $w$

Divide both sides by 14: $\frac{56}{14}=\frac{14w}{14}$, so $w = 4$ cm.

Answer:

$4$ cm