Question

Kathy saves $1 on the first day, $2 on the second day, $3 on the third day and so

on, saving an extra $1 on each subsequent day. On which day will she have $200
or more in total?

Answer 1

Answer: 20 days

Explanation:

Answer 2

We can start by finding the total amount of money Kathy saves each day. On the first day, she saves $1. On the second day, she saves $2, and so on. Therefore, on the nth day, she saves n dollars.

To find out on which day Kathy will have $200 or more in total, we need to find the value of n that satisfies the following inequality:

1 + 2 + 3 + ... + n ≥ 200

This inequality can be rewritten as:

n(n+1)/2 ≥ 200

Multiplying both sides by 2 gives:

n^2 + n ≥ 400

Rearranging gives:

n^2 + n - 400 ≥ 0

Using the quadratic formula, we can solve for n:

n = (-1 ± sqrt(1 + 4*400))/2

n = (-1 ± 41)/2

Since we are looking for a positive value of n, we can ignore the negative solution and get:

n = (-1 + 41)/2 = 20

Therefore, Kathy will have $200 or more in total on the 20th day.