A lottery win is inversely proportional to the number of tickets matching the correct numbers. If 20 tickets have the correct numbers, the winners each receive £1400. One week, each person receives £3500. How many tickets matched the correct numbers?

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Answer: 8

Step-by-step explanation:

Given

lottery win is inversely proportional to the number of tickets matching the correct number.

Suppose lottery amount is given by A and no. of tickets by n then

[tex]\Rightarrow A\propto \frac{1}{n}\\\Rightarrow A\cdot n=\text{constant}[/tex]

Initially A=£1400, n=20

then A=£3500, n=?

Product in both the case is same

[tex]\therefore \quad 1400\times 20=3500\timesn\\\Rightarrow n=8[/tex]

There are 8 tickets that matched the correct numbers