Final Answer-Explanation:
Let's denote the number of type A bulbs as "x" and the number of type B bulbs as "y".
The total cost of buying type A bulbs is 56x.
The total cost of buying type B bulbs is 56y.
The total cost of buying all the bulbs is 2872.
So, we can write the following equation to represent the total cost:
56x + 56y = 2872
We also know that the trader bought a total of x + y bulbs.
Considering that two types of bulbs were bought, we have the following equation:
x + y = total number of bulbs
Now we have a system of two equations:
56x + 56y = 2872
x + y = total number of bulbs
To solve for x, we can rearrange the second equation to express y in terms of x:
y = total number of bulbs - x
Now we can substitute y in the first equation:
56x + 56(total number of bulbs - x) = 2872
56x + 56(total number of bulbs) - 56x = 2872
56(total number of bulbs) = 2872
56(total number of bulbs) = 56
total number of bulbs = 2872 / 56
total number of bulbs = 51
Now that we know the total number of bulbs, we can use this information to solve for x:
x + y = 51
x + (51 - x) = 51
x + 51 - x = 51
51 = 51
So, it seems like we have encountered an inconsistency in our solution attempt. Let's revisit our initial model of the problem.
Let's denote the number of type A bulbs as "x" and number of type B bulbs as "y".
Given the total number of bulbs is 51, we have:
x + y = 51
Now, let's use the total cost of buying the bulbs:
56x + 56y = 2872
56x + 56(51 - x) = 2872
56x + 56*51 - 56x = 2872
56*51 = 2872
x = 2872 - 56*51
x = 2872 - 2856
x = 16
So according to the calculations, the trader bought 16 type A bulbs.
