A flooring company uses 8 nails for every square foot of hardwood installed. If 2,000 nails have already been used and the maximum available is 5,000 nails, how many more square feet can be installed before running out of nails?

What the rate tells you

“8 nails for every square foot” is a unit rate, meaning it takes 8 nails to install $1\text{ ft}^2$. To find how much more flooring can be installed, we first need the number of nails still available.

Find the remaining nails

Maximum nails available: $5{,}000$

Already used: $2{,}000$

Remaining: $$5{,}000-2{,}000=3{,}000 \text{ nails}$$

Convert nails left into square feet

If $8$ nails are needed per square foot, then the number of square feet possible is: $$\frac{3{,}000\text{ nails}}{8\text{ nails/ft}^2}=375\text{ ft}^2$$

Quick check

$375\text{ ft}^2 \times 8 = 3{,}000$ nails, which matches the nails left, so the result is consistent.