MHB Problems leading to quadratic equation

[NotaMathPerson]

a man spent 78 dollars for cigarettes. has the price per box been .50 cents less, he could have had one more box. How many boxes did he buy?

Heres what I tried

let $y=$ original price per box
$y-50=$ new price per box

Now,

$\frac{780}{y}=$ original number of boxes bought
$\frac{780}{y-50}=$ new number of boxes bought$\frac{780}{y-50}=\frac{780}{y}+1=$

$y^2-50y-39000=0$

Solving for y I get decimal number.

Can you tell me where my mistake is?

Thanks!

All variables are y. I edited it.

 

[MarkFL]

I would let $B$ be the number of boxes he bought...and $P$ be the price (in dollars) per box, such that we may state:

$$BP=78$$

$$(B+1)\left(P-\frac{1}{2}\right)=78$$

I am assuming you meant "had the price per box been 50 cents less."

Solving the first equation for $P$ and substituting into the second, we obtain:

$$(B+1)\left(\frac{78}{B}-\frac{1}{2}\right)=78$$

Multiply through by $2B\ne0$:

$$(B+1)(156-B)=156B$$

Expand and write in standard form:

$$B^2+B-156=0$$

Factor:

$$(B+13)(B-12)=0$$

Discard the negative root, and we have:

$$B=12$$

 

[NotaMathPerson]

Hello MarkFl!

Can you tell what I did wrong in my attempt above?

 

[MarkFL]

Hello MarkFl!

Can you tell what I did wrong in my attempt above?

Well, you are being asked for the number of boxes, so you want to get an equation using a variable that represents the number of boxes. That's more direct than solving for the price...but you can answer the question this way.

In your equations you should be using 7800 instead of 780, since you are using cents instead of dollars. See if that fixes things...:D

 

[NotaMathPerson]

Well, you are being asked for the number of boxes, so you want to get an equation using a variable that represents the number of boxes. That's more direct than solving for the price...but you can answer the question this way.

In your equations you should be using 7800 instead of 780, since you are using cents instead of dollars. See if that fixes things...:D

Oh yes! That careless mistake. Thank you very much!