To determine the number of nails and bolts in the toolbox, we first need to express the quantities of nails, screws, and bolts in terms of a common variable.
Given the ratio of nails to screws to bolts is \(5:3:2\), we can let:
- The number of nails be \(5x\),
- The number of screws be \(3x\),
- The number of bolts be \(2x\).
From the problem, we know there are 15 screws in the toolbox. Therefore, we can set up the equation based on the number of screws:
\[ 3x = 15 \]
Now, we can solve for \(x\):
\[ x = \frac{15}{3} = 5 \]
Now that we have the value of \(x\), we can find the numbers of nails and bolts:
-
Number of nails: \[ 5x = 5 \times 5 = 25 \]
-
Number of bolts: \[ 2x = 2 \times 5 = 10 \]
Thus, in the toolbox, there are:
- 25 nails
- 15 screws
- 10 bolts
Final counts:
- Nails: 25
- Screws: 15
- Bolts: 10
1 answer