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

'Great choice! If you buy 2 more flowers, you'll get a discount and only have to pay z dollars in total.'

The girl thought about it and decided to take the offer. She bought 2 more flowers and paid z dollars for all the flowers.

Let's try to find the values of x, y, and z.

We know that the girl bought x flowers for y dollars initially, so the cost of each flower is y/x dollars.

When she bought 2 more flowers, the total number of flowers she bought became x + 2.

The new cost of each flower, after the discount, is z/(x + 2) dollars.

Since the cost of each flower remained the same even after the discount, we have the equation:

y/x = z/(x + 2)

We can cross-multiply to get:

y(x + 2) = zx

Expanding this equation gives us:

xy + 2y = zx

Now, let's try to simplify this equation further.

xy + 2y = zx
xy + 2y - zx = 0
y(x + 2 - z) = 0

For this equation to hold true, either y = 0 or (x + 2 - z) = 0.

If y = 0, it means the girl didn't pay anything for the flowers. However, since y is the cost of the flowers, this scenario doesn't make sense.

Therefore, we must have (x + 2 - z) = 0.

Simplifying this equation gives us:

x + 2 = z

So, the value of z is x + 2.

Therefore, the girl paid x + 2 dollars for the flowers after the discount.

In conclusion, the values of x, y, and z are related by the equation y(x + 2) = zx, and z = x + 2.

Answer

5,1

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