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Billy is 5'10" and weighs 150 pounds.

Calculate which is more valuable:

- A pile of pennies equaling his weight, or
- A stack of quarters equaling his height?

Note:
- A penny weighs 2.5 grams.
- There are 453.59237 grams in each pound.
- A quarter laid flat is 0.069 inches thick.

A. A pile of pennies weighing 150 pounds.
B. A stack of quarters standing 5'10" high.

Answer :

Sure! Let's break down the problem step by step to find out which is more valuable, a pile of pennies equaling Billy's weight or a stack of quarters equaling his height.

### Step 1: Weight of the Pennies

1. Billy's weight in pounds: 150 pounds
2. Weight of one pound in grams: 453.59237 grams
3. Weight of Billy in grams: [tex]\( 150 \text{ pounds} \times 453.59237 \text{ grams per pound} \)[/tex]
4. Weight of one penny: 2.5 grams
5. Number of pennies: [tex]\( \text{Total weight in grams} \div \text{Weight of one penny} \)[/tex]
6. Value of the pennies: [tex]\( \text{Number of pennies} \times \$0.01 \)[/tex]

Performing these calculations, we get:

- Weight of Billy in grams: [tex]\( 150 \times 453.59237 = 68038.8555 \)[/tex] grams
- Number of pennies: [tex]\( 68038.8555 \div 2.5 = 27215.5422 \)[/tex]
- Value of the pennies: [tex]\( 27215.5422 \times 0.01 = 272.155422 \)[/tex] dollars

### Step 2: Height of the Quarters

1. Billy's height: 5 feet 10 inches
2. Convert height to inches: [tex]\( 5 \times 12 \text{ inches per foot} + 10 \)[/tex] inches
3. Height of one quarter in inches: 0.069 inches
4. Number of quarters: [tex]\( \text{Total height in inches} \div \text{Height of one quarter} \)[/tex]
5. Value of the quarters: [tex]\( \text{Number of quarters} \times \$0.25 \)[/tex]

Performing these calculations, we get:

- Total height in inches: [tex]\( 5 \times 12 + 10 = 70 \)[/tex] inches
- Number of quarters: [tex]\( 70 \div 0.069 = 1014.4927536231884 \)[/tex]
- Value of the quarters: [tex]\( 1014.4927536231884 \times 0.25 = 253.62318840579707 \)[/tex] dollars

### Conclusion

After comparing the values, we find:

- Value of the pile of pennies equaling Billy's weight: \[tex]$272.155422
- Value of the stack of quarters equaling Billy's height: \$[/tex]253.62318840579707

The pile of pennies equaling Billy's weight is more valuable at \[tex]$272.16 compared to the stack of quarters equaling his height at \$[/tex]253.62.

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