Build a ramp
His grandmother can't climb her porch steps anymore. The porch is 30 inches off the ground. He will build her a ramp. How long must it be?
The rule
A safe ramp goes up 1 inch for every 12 inches it runs.
up / across = 1 / 12
Put in what he knows
Up is 30. Across is what he needs. Call it x.
30 / x = 1 / 12
Solve for x
Cross multiply.
1 · x = 30 · 12
x = 360
The answer
360 inches. That is 30 feet.
He knows it before he buys one board. Too short and the ramp is too steep and not safe.Keep building
The ramp is 36 inches wide. The yard is only 20 feet deep. A board costs $9.
How much wood? How much money? Where does it turn?
It is all the same kind of math you practice here: slope, and solving for x.