set 1. For every 37 tickets she sold, Martine was given a free ticket for one of the children. If 33 175 children wanted to go, how many tickets did Martine have to sell?

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UpStudy AI · Accepted Answer

To solve the problem, we need to determine how many tickets Martine had to sell in order to provide free tickets for all 175 children.

1. **Identify the known conditions:**
   - For every 37 tickets sold, Martine gets 1 free ticket.
   - There are 175 children who want to go.

2. **Calculate the number of free tickets needed:**
   Since each child needs a ticket, Martine needs to provide 175 tickets.

3. **Determine how many tickets Martine needs to sell to get enough free tickets:**
   Let $$ x $$ be the number of tickets Martine needs to sell. The number of free tickets she gets is given by the formula:
   $$
   \text{Free tickets} = \frac{x}{37}
   $$
   To find the total number of tickets (sold + free) that Martine needs to cover all 175 children, we can set up the equation:
   $$
   x + \frac{x}{37} = 175
   $$

4. **Solve the equation:**
   To eliminate the fraction, multiply the entire equation by 37:
   $$
   37x + x = 175 \times 37
   $$
   Simplifying gives:
   $$
   38x = 6475
   $$
   Now, divide both sides by 38:
   $$
   x = \frac{6475}{38}
   $$

Now, let's calculate $$ x $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{6475}{38}$$
Calculating $$ x $$ gives us:

$$
x = \frac{6475}{38} \approx 170.39
$$

Since Martine cannot sell a fraction of a ticket, we round up to the nearest whole number. Therefore, Martine needs to sell at least 171 tickets to ensure that all 175 children can go.

**Final Answer:**
Martine has to sell **171 tickets**.
Martine needs to sell 171 tickets to provide free tickets for all 175 children.

set 1. For every 37 tickets she sold, Martine was given a free ticket for one of the children. If 33 175 children wanted to go, how many tickets did Martine have to sell?

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