我娃做worksheet时遇到这个题来问我，我解答出来后和worksheet提供的答案不一样，不知道是我错了还是答案错了。所以抄出来给大家做做 a boy saved 43 more nickels than dimes. after he spent 17 dimes, he had twice as many nickels than dimes. how many coins did he have left ?
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: The boy has 43 more nickels than dimes, so n=d+43n = d + 43n=d+43. 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.
