https://file.aiquickdraw.com/mathbot/file/1726007536118omz6qs5u.jpg

Let's break down the problem step by step.

### Problem Summary:
You are tasked with making 100 treat bags. Each bag should contain:
- 1 piece of chocolate,
- 1 sucker, and
- 1 stick of gum.

The candy is packaged in specific amounts:
- Chocolate: 36 pieces per package,
- Suckers: 24 suckers per package,
- Gum: 15 sticks per package.

### Questions:
1. What is the minimum number of packages of each candy that needs to be purchased to make at least 100 treat bags?
2. How many treat bags will you be able to make with the candy you buy?
3. Will there be any leftover candy? If so, how much?

### Step-by-Step Solution:

#### 1. Chocolate:
- One package of chocolate has 36 pieces.
- To find out how many packages are needed for 100 treat bags:
  \[
  \text{Number of packages} = \frac{100}{36} = 2.78
  \]
  Since you cannot buy a fraction of a package, you'll need **3 packages** of chocolate.

- **Total pieces of chocolate** in 3 packages:
  \[
  3 \times 36 = 108 \text{ pieces of chocolate}.
  \]
  
#### 2. Suckers:
- One package of suckers contains 24 suckers.
- To find the number of packages needed for 100 treat bags:
  \[
  \frac{100}{24} = 4.17
  \]
  You'll need **5 packages** of suckers.

- **Total suckers** in 5 packages:
  \[
  5 \times 24 = 120 \text{ suckers}.
  \]

#### 3. Gum:
- One package of gum has 15 sticks.
- To find the number of packages needed for 100 treat bags:
  \[
  \frac{100}{15} = 6.67
  \]
  You'll need **7 packages** of gum.

- **Total sticks of gum** in 7 packages:
  \[
  7 \times 15 = 105 \text{ sticks of gum}.
  \]

### Summary of Purchases:
- **Chocolate:** 3 packages (108 pieces)
- **Suckers:** 5 packages (120 suckers)
- **Gum:** 7 packages (105 sticks)

### Number of Treat Bags You Can Make:
Since each treat bag needs one of each item, the limiting factor is chocolate (since you have 108 pieces). Therefore, you can make **108 treat bags** in total.

### Leftover Candy:
- **Chocolate:** No leftovers (all 108 pieces used).
- **Suckers:** You bought 120 suckers, so:
  \[
  120 - 108 = 12 \text{ suckers leftover}.
  \]
- **Gum:** You bought 105 sticks of gum, so:
  \[
  105 - 108 = -3
  \]
  (but this means there will be no leftovers for gum, as the limiting factor is still 108 bags).

---

Would you like further details or clarifications? 

Here are five related questions you might find helpful:
1. What if you needed to make 200 treat bags instead?
2. How would the calculations change if gum came in larger packs of 30?
3. What is the total cost if you know the price of each package?
4. How could you minimize leftovers by adjusting the quantities purchased?
5. What is the greatest common divisor (GCD) of the package sizes, and how could it help in reducing waste?

**Tip:** When working with packages, rounding up is essential since you can't purchase a fraction of a package.

We have been asked to make 100 treat bags containing a piece of chocolate, a sucker, and a stick of gum. There are 36 pieces of chocolate in a package. Suckers come in packs of 24 and gum in packs of 15 sticks. What is the minimum number of packages of each type of candy that should be purchased to make enough treat bags? How many treat bags will it make? Will there be any left over? If so, how many?

Find out how many packages of chocolate, suckers, and gum are needed to make 100 treat bags. Includes step-by-step calculation using division and rounding, with details on leftover candy. Suitable for middle school students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation