A girl entered a store and bought x flowers for y dollars (x and y are integers). When she was about to leave, the clerk said, “If you buy 10 more flowers I will give you all for $$2, and you will save 80 cents a dozen”. The values of x and y are?a)(15,1)b)(10,1)c)(5,1)d)Cannot be determined from the given information.Correct answer is option 'C'. Can you explain this answer?

Question

A girl entered a store and bought x flowers for y dollars (x and y are integers). When she was about to leave, the clerk said, &ldquo;If you buy 10 more flowers I will give you all for $$2, and you will save 80 cents a dozen&rdquo;. The values of x and y are?a)(15,1)b)(10,1)c)(5,1)d)Cannot be determined from the given information.Correct answer is option 'C'. Can you explain this answer?

Answer

Explanation:
The girl initially bought x flowers for y dollars.

Given Information:
- She bought x flowers for y dollars.
- If she buys 10 more flowers, she can get all the flowers for $2 and save 80 cents a dozen.
Let's break down the given information step by step:

Step 1: Initial Purchase
- Initial purchase: x flowers for y dollars.

Step 2: Additional Purchase
- If she buys 10 more flowers, the total cost becomes $2.
- She saves 80 cents a dozen, which means she saves 80 cents for every 12 flowers.
- This implies that the cost of 12 flowers is reduced by 80 cents.
- Since she bought 10 more flowers, the cost of these 10 flowers is reduced by 80/12 = 6.67 cents.

Step 3: Calculation
- Let's assume the cost of each flower is z cents.
- Initially, the cost of x flowers is y dollars.
- After buying 10 more flowers, the total cost becomes $2.
- So, the cost of x + 10 flowers is y + 2 dollars.
- Additionally, she saves 6.67 cents on the 10 extra flowers.
- Therefore, the cost of 10 flowers is 10z - 6.67 cents.
- Given that the total cost of x + 10 flowers is $2, we can form the following equation:
xz + 10z - 6.67 = 200 cents.

Step 4: Determine the values of x and y
- Since x, y, and z are integers, we need to find a combination of x and y that satisfies the equation above.
- By trial and error, we find that x = 5 and y = 1 satisfy the equation.
Therefore, the values of x and y are (5, 1), which corresponds to option C.

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