A dealer bought some radios for a total of $1,200. She gave away 6 radios as gifts, sold each of the rest for $10 more than she paid for each radio, and broke even. How many radios did she buy?

original price for x radios is 1200/x

So,

(x-6)(1200/x + 10) = 1200

30

To solve this problem, we can set up an equation based on the given information.

Let's assume the dealer initially bought 'x' radios.

The total cost of buying x radios would be x multiplied by the price she paid for each radio. Since she bought radios for $1,200 in total, we have the equation:

price per radio * number of radios = total cost
x * price per radio = $1,200

Next, we know that she gave away 6 radios as gifts, which means she sold (x - 6) radios.

She sold each radio for $10 more than she paid for it, so the selling price per radio would be:

price per radio + $10

Since she broke even, the total amount she received from selling the radios would be equal to the total amount she spent to buy them:

selling price per radio * number of sold radios = total cost
(x - 6) * (price per radio + $10) = $1,200

Now we have two equations:

1) x * price per radio = $1,200
2) (x - 6) * (price per radio + $10) = $1,200

We need to solve this system of equations to find the value of x, which represents the number of radios she bought.