Question

the hole for a fence post needs to be 5 feet deep. it is currently 2 feet 8 inches deep. how much deeper must the hole be? use pencil and paper. show two ways to solve this problem. use the relationship 12 inches = 1 foot. the hole needs to be \boxed{} inches deeper.

Explanation:

Step1: Convert feet to inches

We know that \(1\) foot \( = 12\) inches. So, \(5\) feet is \(5\times12 = 60\) inches and \(2\) feet is \(2\times12=24\) inches. The current depth is \(2\) feet \(4\) inches, so we convert \(2\) feet to inches (\(24\) inches) and add \(4\) inches, so current depth \(= 24 + 4=28\) inches.

Step2: Calculate the difference

We need to find how much deeper the hole needs to be. The desired depth is \(60\) inches and current depth is \(28\) inches. So the difference is \(60 - 28 = 32\) inches.

Another way:

Step1: Find the difference in feet first

Desired depth is \(5\) feet, current depth is \(2\) feet \(4\) inches. The difference in feet is \(5 - 2=3\) feet, but we have an extra \(4\) inches to consider. Wait, no, actually, we can convert the \(3\) feet to inches (\(3\times12 = 36\) inches) and then subtract the \(4\) inches (because the current depth is \(2\) feet \(4\) inches, so the remaining after \(2\) feet is \(4\) inches, so from \(2\) feet \(4\) inches to \(5\) feet, we need \(3\) feet minus \(4\) inches? Wait, no, better to do as first method. Wait, first method: desired depth \(5\) feet \(= 60\) inches, current \(2\) feet \(4\) inches \(= 28\) inches, difference \(60 - 28 = 32\) inches.

Answer:

\(32\)