Question

There were 14 lollipops more than chocolate bar in a candy shop. 2/5 of the chocolate bars and 3/7 of lollipops were sold. given that there were 213 chocolate bars and lollipops left, how many chocolate bars were there in the candy shop at first?

Answer 1

The problem involves defining variables for the number of chocolate bars and lollipops, setting up an equation based on the given conditions, and solving for the number of chocolate bars. Through step-by-step calculation, we find that there were originally 175 chocolate bars in the candy shop.

Step-by-step explanation:

Let's define the number of chocolate bars as C and the number of lollipops as L. According to the problem, there were 14 more lollipops than chocolate bars, so we can express the number of lollipops as L = C + 14.

Since 2/5 of the chocolate bars were sold, then 3/5 were left. Similarly, with 3/7 of the lollipops sold, 4/7 were left. So we can write the following equations based on what was left:

• (3/5) * C for the chocolate bars
• (4/7) * (C + 14) for the lollipops

The total number of candies left is 213. Therefore we have the equation: (3/5) * C + (4/7) * (C + 14) = 213

Now let's solve the equation step by step:

1. Multiply through by 35 (the least common multiple of 5 and 7) to get rid of the fractions:
   21 * C + 20 * (C + 14) = 7,455
2. Expand and combine like terms:
   21C + 20C + 280 = 7,455
3. Simplify:
   41C = 7,175
4. Divide by 41 to solve for C:
   C = 175

So, there were 175 chocolate bars in the candy shop at first.