Question

Gaby's piggy bank contains nickels and dimes worth $6.15. If she has 78 coins in all, how many of each does she have

Answer 1

To determine how many nickels and dimes Gaby has in her piggy bank, we create two linear equations from the given information and solve them simultaneously. Gaby has 33 nickels and 45 dimes.

Step-by-step explanation:

The subject of this question is Mathematics, specifically related to algebra and problem-solving with systems of linear equations. To solve the problem about Gaby's piggy bank containing nickels and dimes worth $6.15 with a total of 78 coins, we can set up two equations based on the information given.

Let's represent the number of nickels as n and the number of dimes as d. We can write the first equation based on the total number of coins:

• n + d = 78

And the second equation based on the total value of the coins (converting the dollar amount to cents to avoid decimals):

• 5n + 10d = 615

Now, we can solve these equations simultaneously to find the values of n and d.

Step 1: Multiply the first equation by 5 to prepare for elimination:

• 5n + 5d = 390

Step 2: Subtract this new equation from the second equation:

• (5n + 10d = 615) - (5n + 5d = 390)
• 5d = 225
• d = 45

Step 3: Substitute d = 45 back into the first equation:

• n + 45 = 78
• n = 78 - 45
• n = 33

Therefore, Gaby has 33 nickels and 45 dimes in her piggy bank.