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Let's work through the problem step by step.

We are given the following information:

- There are 280 sweets in total.
- The ratio of green sweets to orange sweets is 2:3.
- The ratio of orange sweets to yellow sweets is 1:5.

Let:
- \( g \) be the number of green sweets,
- \( o \) be the number of orange sweets,
- \( y \) be the number of yellow sweets.

### Step 1: Express the ratios in terms of variables

From the first ratio:
\[
\frac{g}{o} = \frac{2}{3}
\]
This gives:
\[
g = \frac{2}{3}o
\]

From the second ratio:
\[
\frac{o}{y} = \frac{1}{5}
\]
This gives:
\[
y = 5o
\]

### Step 2: Use the total number of sweets

We know the total number of sweets is 280, so:
\[
g + o + y = 280
\]

Substitute the expressions for \( g \) and \( y \) in terms of \( o \):
\[
\frac{2}{3}o + o + 5o = 280
\]

### Step 3: Solve for \( o \)

Combine like terms:
\[
\left( \frac{2}{3}o + o + 5o \right) = \frac{2}{3}o + \frac{3}{3}o + \frac{15}{3}o = \frac{20}{3}o
\]

Now solve for \( o \):
\[
\frac{20}{3}o = 280
\]
Multiply both sides by 3:
\[
20o = 840
\]
Divide by 20:
\[
o = 42
\]

### Step 4: Find the number of green sweets

Now that we know \( o = 42 \), we can find the number of green sweets:
\[
g = \frac{2}{3} \times 42 = 28
\]

### Step 5: Verify with the total number of sweets

Now, find \( y \):
\[
y = 5 \times 42 = 210
\]

Check the total:
\[
g + o + y = 28 + 42 + 210 = 280
\]
This is correct!

### Final Answer:
There are **28 green sweets** in the box.

Do you want more details on any of the steps, or do you have any questions?

Here are some related questions to expand on:
1. How many orange sweets are there in the box?
2. What percentage of the total sweets are green?
3. If 20 more green sweets were added, how would the ratios change?
4. What is the new total if the number of yellow sweets is doubled?
5. Can you represent this problem using a bar model?

**Tip**: When solving ratio problems, always look to express everything in terms of one variable for easier calculation!

In a box, there are only green sweets, orange sweets, and yellow sweets. There are 280 sweets in total, with the ratio of green sweets to orange sweets as 2:3 and the ratio of orange sweets to yellow sweets as 1:5. Work out how many green sweets there are in the box.

Learn how to solve a sweets ratio problem involving green, orange, and yellow sweets in a box. The total number of sweets is 280, and the problem involves determining the number of green sweets using given ratios. Suitable for students in Grades 8-10.

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