A charity sold 140 lottery tickets for a charity. In the end a total of € 2001 was raised. In the week prior to the draw, given that there were enough tickets left to sell, it was decided to sell them at half the price.

**How much money was raised for the sale of tickets in the last week?**

#### Solution

We know they are sold **x** tickets to **Y** euros and **140-x** tickets to **and / 2** euros

Where we get the following equation that we will simplify:

xy + (140-x) y / 2 = 2001

xy + (140y-xy) / 2 = 2001

2xy + 140y-xy = 4002

xy + 140y = 4002

y (x + 140) = 4002

y = 4002 / (x + 140)

We decompose 4002 = 2 * 3 * 23 * 29

x + 140 must be a divisor number of 4002, so we will have to find out what it is.

The dividers of 4002 are: 2, 3, 23, 29, 6, 46, 58, 69, 87, 138, 174

Since all are less than 140 except the last one,

x + 140 = 174 x = 34; y = 4002/174 = 23

Then 34 * 23 = 782 euros were collected at the initial price and 2001 - 782 = **1219 euros in the last week**.