Michael runs a weekly lottery - Junior Cycle Mathematics - Question 2 - 2019

To determine the least number of lotteries required to achieve over €1000 in profit, we start by setting up the following inequality:

Profit from n lotteries > €1000

Using the profit from one lottery,

n × €320 > €1000.

Now, we solve for n:

n > rac{1000}{320}

Calculating this gives:

$n > 3.125$

Since n must be a whole number, we round up to the nearest whole number, which gives:

n = 4.

Thus, Michael must run at least 4 lotteries to make over €1000 in profit.

To simplify the ratio 25,000 : 45,000, we can divide both numbers by their greatest common divisor, which is 5,000:

$\frac{25000}{5000} : \frac{45000}{5000}$

This simplifies to:

5 : 9.

Thus, the ratio in simplest form is 5 : 9.

To compare the two jackpots, we start by converting the Irish jackpot from euros to dollars using the given exchange rate:

Exchange rate: €1 = $1.15

The Irish jackpot is €4.8 million, so in dollars, it is:

$4.8 \text{ million} \times 1.15 = 5.52 \text{ million dollars}$

The American jackpot is $5.3 million. Since$5.52 million is greater than $5.3 million, we can conclude that:

The Irish jackpot is worth more than the American one.

To find an exchange rate that would make the American jackpot worth more than the Irish one, we need to set up the inequality based on the given jackpots:

Let the new exchange rate be €1 = x dollars.

The value of the Irish jackpot in dollars would then be:

€4.8 million × x.

We want this to be less than the American jackpot:

€4.8 million × x < $5.3 million.

Solving for x gives:

$x < \frac{5.3 \text{ million}}{4.8 \text{ million}}$

Calculating this gives:

$x < 1.1041667$

An example exchange rate that satisfies this condition is €1 = $1.10. Thus:

€1 = $1.10 would make the American jackpot worth more than the Irish one.