Jutiet is painting figuriness of superheroes as part of an art project. She paints 3 figuriness per day for the first 5 days of the project. Realizing that she needs to finish sooner, Jutiet increase her workload to paint 5 figurines per day for the remaining duration of the project. She plans to sell 80% of the figurines. What is the least number of days Jutiet needs to paint figurines for the rest of the project in order to sell at least 112 figurines?

Options

A. `23`
B. `25`
C. `27`
D. `28`

Answer

To solve the problem step by step, let's break it down:

1. **Calculate the number of figurines painted in the first 5 days:**
- Juliet paints 3 figurines per day for the first 5 days.
- Total figurines painted in the first 5 days = 3 figurines/day × 5 days = 15 figurines.

**Hint:** Multiply the number of figurines painted per day by the number of days to find the total.

2. **Let X be the number of figurines painted per day for the remaining days:**
- After the first 5 days, Juliet increases her workload to paint X figurines per day.
- Let the number of days she paints X figurines be D.
- Total figurines painted in the remaining days = X figurines/day × D days = X * D figurines.

3. **Set up the equation for total figurines painted:**
- Total figurines painted = Figurines from the first 5 days + Figurines from the remaining days.
- Total figurines = 15 + X * D.

4. **Determine the total figurines needed to sell at least 112 figurines:**
- Juliet plans to sell 80% of the total figurines she paints.
- Let Y be the total number of figurines she needs to paint.
- We know that 80% of Y must be at least 112 figurines.
- Therefore, 0.8Y = 112.
- To find Y, rearrange the equation: Y = 112 / 0.8 = 140 figurines.

**Hint:** To find Y, divide the number of figurines you want to sell by the percentage you plan to sell.

5. **Set up the equation with the total figurines needed:**
- Now we have the equation: 15 + X * D = 140.

6. **Solve for X * D:**
- Rearranging gives us: X * D = 140 - 15 = 125.

7. **Determine the daily painting rate:**
- Juliet increases her painting rate to 5 figurines per day, so X = 5.
- Substitute X into the equation: 5 * D = 125.

8. **Solve for D:**
- D = 125 / 5 = 25 days.

Thus, the least number of days Juliet needs to paint figurines for the rest of the project is **25 days**.