1. ## math word problem

A boy sold 100 tickets in five days. Each day he sold 6 more tickets than he had sold the previous day. How many tickets did he sell on the first day?

2. Hello, Amy!

A boy sold 100 tickets in five days.
Each day he sold 6 more tickets than he had sold the previous day.
How many tickets did he sell on the first day?
This could be solved as an Arithmetic Sequence, but we'll do it the easy way . . .

Let $\displaystyle x$ = number tickets he sold the first day.

Then: .$\displaystyle \begin{array}{ccc}x+6 &=& \text{tickets sold the 2nd day} \\ x+12 &=& \text{tickets sold the 3rd day} \\ x+18 &=& \text{tickets sold the 4th day} \\ x+24 &=&\text{tickets sold the 5th day} \end{array}$

He sold a total of: .$\displaystyle x + (x+6) + (x+12) + (x+18) + (x+24) \:=\:5x + 60$ tickets.

We are told that he sold 100 tickets.

There is our equation! . . . $\displaystyle 5x + 60 \:=\:100$

. . and we have: .$\displaystyle 5x \:=\:40\quad\Rightarrow\quad x \:=\:8$

Therefore, he sold 8 tickets the first day.