ChatGPT says:

Let's break down the problem step by step to find out how many coins the boy has left.

Step 1: Define Variables

Let:

• ddd = the original number of dimes.
• nnn = the original number of nickels.

According to the problem:

1. The boy has 43 more nickels than dimes, so n=d+43n = d + 43n=d+43.
2. After spending 17 dimes, the boy has twice as many nickels as dimes.

Step 2: Set Up the Equation

After spending 17 dimes, the number of dimes left is d−17d - 17d−17. According to the problem, the number of nickels left is still nnn, and this is twice the number of dimes left:

n=2(d−17)n = 2(d - 17)n=2(d−17)

Step 3: Substitute the First Equation into the Second

We know that n=d+43n = d + 43n=d+43, so we substitute this into the second equation:

d+43=2(d−17)d + 43 = 2(d - 17)d+43=2(d−17)

Step 4: Solve for ddd

Expand and solve the equation:

d+43=2d−34d + 43 = 2d - 34d+43=2d−34

Subtract ddd from both sides:

43=d−3443 = d - 3443=d−34

Add 34 to both sides:

d=77d = 77d=77

So, the boy originally had 77 dimes.

Step 5: Find the Number of Nickels

Using the equation n=d+43n = d + 43n=d+43:

n=77+43=120n = 77 + 43 = 120n=77+43=120

So, the boy originally had 120 nickels.

Step 6: Calculate the Number of Coins Left

After spending 17 dimes, the boy has:

77−17=60 dimes left77 - 17 = 60 \text{ dimes left}77−17=60 dimes left

He still has 120 nickels.

Step 7: Total Number of Coins Left

The total number of coins left is:

60 dimes+120 nickels=180 coins60 \text{ dimes} + 120 \text{ nickels} = 180 \text{ coins}60 dimes+120 nickels=180 coins

So, the boy has 180 coins left.