Answer: the amount of Matthew's sixth paycheque will be $3417.20
Explanation:
o determine the amount of Matthew's sixth paycheque, we can use the given information that his paycheque increases by 50% every month.
Let's start by calculating the amount of his second paycheque. We know that his first paycheque is $450. To find the second paycheque, we need to increase it by 50%.
To increase something by 50%, we multiply it by 1 plus 50% (or 0.5).
So, the second paycheque will be: $450 + ($450 * 0.5) = $450 + $225 = $675.
Now, let's move on to the third paycheque. We'll take the second paycheque of $675 and increase it by 50% again.
The third paycheque will be: $675 + ($675 * 0.5) = $675 + $337.50 = $1012.50.
We can continue this process to find the fourth, fifth, and sixth paycheques. Each time, we'll take the previous paycheque and increase it by 50%.
The fourth paycheque will be: $1012.50 + ($1012.50 * 0.5) = $1012.50 + $506.25 = $1518.75.
The fifth paycheque will be: $1518.75 + ($1518.75 * 0.5) = $1518.75 + $759.38 = $2278.13.
Finally, the sixth paycheque will be: $2278.13 + ($2278.13 * 0.5) = $2278.13 + $1139.07 = $3417.20.
Therefore, the amount of Matthew's sixth paycheque will be $3417.20.