Toby buys 40 pairs of socks in packs of 5 pairs of white socks and 3 pairs of black socks. How many pairs of each color does he buy?
5(5+3) pairs = 40 pairs
White 5 10 15 20 25
Black 3 6 9 12 15
Total 8 16 24 32 40
Toby buys 25 pairs of white socks and 15 pairs of black socks.
To find out how many pairs of each color Toby buys, we need to determine the number of packs he purchases.
Let's assume the number of packs of white socks Toby buys is "w," and the number of packs of black socks Toby buys is "b."
Each pack contains 5 pairs of white socks, so the total number of pairs of white socks Toby buys is 5w.
Each pack also contains 3 pairs of black socks, so the total number of pairs of black socks Toby buys is 3b.
Since Toby buys a total of 40 pairs of socks, we can set up the following equation:
5w + 3b = 40
Now let's solve for w and b.
We can start with a possible value for w and determine the corresponding value for b.
Let w = 0, then:
5(0) + 3b = 40
0 + 3b = 40
3b = 40
b = 40/3 = 13.33 (not a whole number)
Since b should be a whole number, let's try another value for w.
Let w = 1, then:
5(1) + 3b = 40
5 + 3b = 40
3b = 40 - 5
3b = 35
b = 35/3 = 11.67 (not a whole number)
Trying another value for w:
Let w = 2, then:
5(2) + 3b = 40
10 + 3b = 40
3b = 40 - 10
3b = 30
b = 30/3 = 10
We have found a value for w and b that satisfies the equation. Toby buys 2 packs of white socks (10 pairs) and 3 packs of black socks (9 pairs).
Therefore, Toby buys 10 pairs of white socks and 9 pairs of black socks.
To find out how many pairs of each color Toby buys, we can follow these steps:
Step 1: Determine the number of socks in each pack
- Toby buys packs of 5 pairs of white socks and 3 pairs of black socks.
- Since a pair consists of 2 socks, the total number of white socks in a pack is 5 pairs * 2 socks per pair = 10 white socks.
- Similarly, the total number of black socks in a pack is 3 pairs * 2 socks per pair = 6 black socks.
Step 2: Calculate the total number of socks Toby buys
- Toby buys 40 pairs of socks.
- So, the total number of socks bought is 40 pairs * 2 socks per pair = 80 socks.
Step 3: Determine the number of pairs of each color
- As we found in Step 1, each pack contains 10 white socks and 6 black socks.
- Since Toby buys 40 pairs of socks, he would have bought a fraction of packs for each color.
- Let's assume w packs of white socks and b packs of black socks were bought.
- So, the white socks bought would be w packs * 10 white socks per pack = 10w white socks.
- And the black socks bought would be b packs * 6 black socks per pack = 6b black socks.
Step 4: Set up equations based on the given information
- According to the problem statement, Toby buys a total of 80 socks (Step 2).
- The total number of white socks (10w) plus the total number of black socks (6b) equals 80 socks.
- So, we have the equation: 10w + 6b = 80.
Step 5: Solve the equation
- To find the unknown values, we need another equation.
- Since Toby buys 40 pairs of socks, it means the total number of packs he buys (w + b) should be equal to 40.
- So, we have the equation: w + b = 40.
- Now, we have a system of equations:
Equation 1: 10w + 6b = 80
Equation 2: w + b = 40
- To solve this system of equations, we can use substitution or elimination method.
- Let's solve it using the elimination method:
Equation 1 multiplied by 1: 10w + 6b = 80
Equation 2 multiplied by (-6): -6w - 6b = -240
- By adding the two equations together:
(10w + 6b) + (-6w - 6b) = 80 + (-240)
4w = -160
w = -40
- Since w represents the number of packs, and we can't have a negative number of packs, this solution is not possible in the given problem context.
Conclusion:
Based on the given information, it seems there is a mistake or inconsistency in the problem statement. Please double-check the problem and provide the correct details if possible.