Describe how you solved the following problem:

I have a jar filled with $100 worth of quarters, nickels, and dimes. I have the same amount of each type of coin. How many total coins do I have in my jar?

first you make sure you have all your variables using same measurement - cents (since it is the smallest)
$100 = 100*100 cents = 100,000 cents 1 quarter = 25 cents 1 nickel = 5 cent 1 dime = 10 cents
the test of your problem said that: you have $100 in i don't know how many coins of quarters, nickels and dimes 100,000 = X * (25+5+10)
we have to find X:
100,000= X *(25+5+10) 100,000= X *40 X= 100,000/40 X = 2,500 coins

Answered by Mihaela | 2024-06-10

To determine the number of quarters, dimes, and nickels needed to reach $100 for each coin type, divide $100 by the value of each coin in cents, and then sum the quantities. This results in a total of 3400 coins in the jar when you add up 400 quarters, 1000 dimes, and 2000 nickels.
How to Solve the Coin Value Problem
To solve the problem of determining the number of quarters, nickels, and dimes in a jar containing $100 worth of each type of coin, where each type of coin has the same total value, we should first understand the value of each coin. A quarter is worth 25 cents, a dime is 10 cents, and a nickel is 5 cents. Since we have an equal total value for each coin type, we can set up an equation where the total value is the product of the number of coins and the value of each coin.
Let's denote the number of quarters, dimes, and nickels as 'q', 'd', and 'n', respectively. Since each type of coin has $100 worth, we can write the following equations:
25q = 100 dollars
10d = 100 dollars
5n = 100 dollars
Converting dollars into cents (since we're dealing with coins) gives us $100 = 10000 cents. We can now solve each of the equations for 'q', 'd', and 'n' to find the number of each type of coin:
25q = 10000 cents => q = 10000 / 25 => q = 400 quarters
10d = 10000 cents => d = 10000 / 10 => d = 1000 dimes
5n = 10000 cents => n = 10000 / 5 => n = 2000 nickels
However, as we're told that the value of each coin type is equal, not the number of coins itself, we have each 'q', 'd', and 'n' representing $100 of their respective coin's total value. To find the total number of coins, we just sum up the individual numbers:
Total Coins = q + d + n = 400 + 1000 + 2000 = 3400 coins in total.
Note that in this situation, having the same amount for each coin type doesn't imply the same number of each coin but the same total value.

Answered by Qwcold | 2024-06-24

By letting x represent the number of each type of coin (quarters, nickels, and dimes), I set up an equation based on their total value of $100 or 10000 cents. Solving the equation, I found that there are 250 of each type of coin, resulting in a total of 750 coins in the jar.
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Answered by Mihaela | 2025-01-10