Explanation:
Given that:
let the number of radios bought = x
The price for a total radio = $1,344
price per radio = 1,344 / x
Number of radio gifted = 8
Number of radio sold = x - 8
She sold the rest radio more than the original price she bought the radio
i.e, $14 more than she paid for each
1344/x + 14
Total amount radio sold = (1344/x + 14) ( x - 8)
![\begin{gathered} (1344)/(x)\text{ + 14 }\cdot\text{ (x - 8)} \\ \frac{1344\text{ + 14x}}{x}\text{ (x - 8)} \\ Open\text{ the parentheses} \\ \frac{1344x\text{ + 1344}\cdot(-8)\text{ + 14x}\cdot x\text{ + 14x (-8)}}{x} \\ \frac{1344x-10752+14x^2\text{ - 112x}}{x} \\ \text{ since it broken even} \\ \frac{1344x-10752+14x^2\text{ - 112x}}{x}\text{ = 1344} \\ \text{Cross multiply} \\ 1344x-10752+14x^2\text{ - 112x = 1344 x} \\ \text{Collect the like terms} \\ 14x^2\text{ + 1344x - 1344x - 112x - 10752 = 0} \\ 14x^2\text{ - 112x - 10752 = 0} \\ \text{Divide through by 14} \\ (14x^2)/(14)\text{ - }(112x)/(14)\text{ - }(10752)/(14)\text{ = }(0)/(14) \\ x^2\text{ - 8x - }1344\text{ = 0} \\ \text{ Using the general quadratic formula to find x} \\ \text{let a = 1, b = -8 and c = -1344} \\ x\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ x\text{ = }\frac{-(-8)\text{ }\pm\sqrt[]{-8^2\text{ - 4 }\cdot\text{ 1 }\cdot(-1344)}}{2\cdot\text{ 1}} \\ x\text{ = }\frac{8\pm\sqrt[]{64\text{ + 5376}}}{2} \\ x\text{ = }\frac{8\pm\sqrt[]{5440}}{2} \\ x\text{ = }\frac{8\text{ }\pm\text{ 73.75}}{2} \\ x\text{ = }\frac{8\text{ + 73.75}}{2}\text{ or }\frac{8\text{ - 73.76}}{2} \\ x\text{ = 81.75/2} \\ x\text{ = 40.875} \\ \text{She bought 41 radios} \\ \text{The price per radio = 1344/x} \\ \text{The price per radio = 1344 / 41} \\ \text{ \$32}.78 \\ \text{She gifted 8} \\ \text{She sold = 41- }8 \\ =\text{ 33} \end{gathered}]()