Question14. A jar contains equal numbers of nickels and dimes. The total value of the coins is . How many coins are in the jar?
Studdy Solution
STEP 1
What is this asking? If a jar has the same number of nickels () and dimes (), and all the coins are worth , how many coins are there in total? Watch out! Don't forget that the question asks for the *total* number of coins, not just the number of nickels or dimes!
STEP 2
1. Calculate the value of one nickel and one dime.
2. Determine the value of a pair of coins.
3. Calculate how many pairs of coins are in the jar.
4. Calculate the total number of coins.
STEP 3
A nickel is worth .
A dime is worth .
Easy peasy!
STEP 4
Since we have an equal number of nickels and dimes, let's think about them in *pairs*.
One nickel plus one dime equals .
So, each **pair** of coins is worth .
STEP 5
The total value of all the coins is .
Since each pair is worth , we can figure out how many pairs are in the jar by dividing the total value by the value of one pair:
There are **27 pairs** of coins in the jar!
STEP 6
Each pair contains two coins (one nickel and one dime).
Since we have 27 pairs, the total number of coins is .
Boom!
STEP 7
There are **54** coins in the jar.
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