Question

The value of my coins if I have p pennies, n nickels and twice as many quarters as pennies.

Answer 1

Answer:

• Total value in cents = 51p+5n
• Total value in dollars = (51p+5n)/100

The answer varies depending if your teacher wants the answer in cents only, or in dollars only.

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Explanation:

• p = number of pennies
• n = number of nickels
• 2p = number of quarters, since we have twice as many quarters compared to pennies.

Based on that, we know,

• p = number of cents from the pennies (1 penny = 1 cent)
• 5n = number of cents from the nickels (5 nickels = 5 cents, multiply both sides by n)
• 25(2p) = 50p = number of cents from the quarters

and ultimately

p+5n+50p = 51p+5n

represents the total value of all the coins, and this value is in cents. We would divide by 100 to convert from cents to dollars. So we can say that 51p+5n cents = (51p+5n)/100 dollars

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As an example, let's say

• p = 4
• n = 5

So we have

• p = 4 pennies
• n = 5 nickels
• q = 2p = 2*4 = 8 quarters

This would mean we have

• p = 4 cents from the pennies only
• 5n = 5*5 = 25 cents from the nickels only
• 25q = 25*8 = 200 cents from the quarters only

Overall we have p+5n+25q = 4+25+200 = 229 cents which converts to 229/100 = $2.29

We can also say 51p+5n = 51*4+5*5 = 204+25 = 229 which is a slight shortcut to get the same result (that result being in cents).