Question

A label that wraps around a box of golf ball covers 75% of its lateral surface area. What is the value of x?

Answer 1

we know the label is 3 inches wide and since the box is 2 inches tall, is the label is 2 inches tall only on the front and back of the box, namely the sides, the LATERAL area, the lateral area for the label doesn't include the top and bottom. How many inches is the label laterally?

`\stackrel{front}{(3\cdot 2)}+\stackrel{back}{(3\cdot 2)}\implies 12` and we know that's 75% of the total lateral area.

what about the total lateral area, how many inches is it?

`\stackrel{front}{(x\cdot 2)}+\stackrel{back}{(x\cdot 2)}\implies 4x`

so, we know that 4x is the 100% of the lateral area, and we also know that 12 is 75% of it.

`\begin{array}{ccll} \stackrel{lateral}{area}&\%\\ \cline{1-2} 4x&100\\ 12&75 \end{array}\implies \cfrac{4x}{12}=\cfrac{100}{75}\implies \cfrac{x}{3}=\cfrac{4}{3} \\\\\\ 3x=12\implies x=\cfrac{12}{3}\implies x=4`