Question

The ratio of nails to screws to bolts in a toolbox is 5:3:2. There are 15 screws in the toolbox. Complete the sentences below.
There are ____________ nails in the toolbox.
The toolbox contains a total of __________ nails, screws and bolts.
explain in words

Answer 1

To determine the number of nails and the total number of items in the toolbox, we start with the given ratio of nails to screws to bolts, which is 5:3:2.

1. **Understanding the ratio:**
- The ratio signifies that for every 5 parts of nails, there are 3 parts of screws and 2 parts of bolts.

2. **Identifying the total parts:**
- We can add the parts of the ratio together:
- 5 (nails) + 3 (screws) + 2 (bolts) = 10 parts total.

3. **Finding the value of each part:**
- Since we know there are 15 screws, and screws correspond to 3 parts in the ratio, we can find the value of one part.
- To find this, we divide the number of screws by the number of parts corresponding to screws:
- 15 screws ÷ 3 parts = 5 screws per part.

4. **Finding the number of nails:**
- Now, since nails are represented by 5 parts in the ratio, we can multiply the number of parts for nails by the value of each part:
- 5 parts (nails) × 5 screws per part = 25 nails.

5. **Finding the number of bolts:**
- We can also find the number of bolts in a similar manner. Bolts correspond to 2 parts in the ratio:
- 2 parts (bolts) × 5 screws per part = 10 bolts.

6. **Calculating the total number of items:**
- Finally, we can calculate the total number of items in the toolbox by adding the number of nails, screws, and bolts:
- Nails (25) + Screws (15) + Bolts (10) = 50 total items.

So, to fill in the blanks:
- There are **25** nails in the toolbox.
- The toolbox contains a total of **50** nails, screws, and bolts.