Final answer:
To solve for the number of eggs Sirak buys, the given equation is set up based on the cost of eggs and bread rolls, leading to a quadratic equation. The number of eggs is represented as (x-2), so the answer Sirak buys (x-2) eggs given that this correctly fits into the cost equation, making option b) x - 2 the correct answer.
Step-by-step explanation:
Sirak buys eggs at (x-2) cents each and (x-2) bread rolls at (x-3) cents each. The problem states that the total bill is 1.75 dollars, which is 175 cents. We need to form an equation to calculate the number of eggs.
The cost for eggs is (x-2) cents per egg multiplied by the number of eggs Sirak buys. The cost for bread rolls is (x-2) bread rolls times (x-3) cents each. Adding these two costs should give us the total bill.
Equation for eggs: (x-2)(number of eggs)
Equation for bread rolls: (x-2)(x-3)
Adding both we get: (x-2)(number of eggs) + (x-2)(x-3) = 175
Since Sirak buys (x-2) eggs:
(x-2)(x-2) + (x-2)(x-3) = 175
x2 - 4x + 4 + x2 - 5x + 6 = 175
2x2 - 9x + 10 - 175 = 0
2x2 - 9x - 165 = 0
This is a quadratic equation, but we don't need to solve for x to find the number of eggs since it's already given in the form of (x-2). We just need to ensure that (x-2) is indeed the correct factor for the number of eggs.