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?

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- Sep 9th 2008, 10:33 AMamywright00math 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?

- Sep 9th 2008, 10:49 AMSoroban
Hello, Amy!

Quote:

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?

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.