Question: Ms. Young made a scale drawing of the community garden in her neighborhood.
The actual lengths of the garden are shown in the table.
Choose an equivalent ratio that shows each length
in the scale drawing to the length in the garden.
Length in
Scale Drawing
Actual Length
in Garden
Ratio
6 in. 24 ft ?
8 in. 32 ft
10 in. 40 ft
6 in.
10 in.
Scale Drawing
8 in.
1. **State the problem:** We need to find the equivalent ratio of each length in the scale drawing to the actual length in the garden.
2. **Write the given data:**
- Scale drawing lengths: $6$ in, $8$ in, $10$ in
- Actual garden lengths: $24$ ft, $32$ ft, $40$ ft
3. **Set up the ratio for the first pair:**
$$\text{Ratio} = \frac{\text{Length in scale drawing}}{\text{Actual length in garden}} = \frac{6}{24}$$
4. **Simplify the ratio:**
$$\frac{6}{24} = \frac{\cancel{6}^1}{\cancel{24}^4} = \frac{1}{4}$$
5. **Check the other pairs to confirm the ratio:**
- For $8$ in and $32$ ft:
$$\frac{8}{32} = \frac{\cancel{8}^1}{\cancel{32}^4} = \frac{1}{4}$$
- For $10$ in and $40$ ft:
$$\frac{10}{40} = \frac{\cancel{10}^1}{\cancel{40}^4} = \frac{1}{4}$$
6. **Conclusion:** The equivalent ratio for each length in the scale drawing to the actual length in the garden is:
$$\boxed{\frac{1}{4}}$$
This means every inch in the scale drawing represents $4$ feet in the actual garden.