Liz wants to earn 650 to purchase a new laptop, so she decides to make bracelets and sell them online. Based on a friend's sales history.Liz knows she can use the expression -5p+115 to estimate the number of bracelets she'll sell given the price per bracelet, p. Which equation can Liz use to estimate the price per bracelet that will earn her 650 in revenue? 650p=p(-5p+115) 650=p(-5p+115) What two prices will earn Liz exactly 650 in revenue? or s

To find the equation Liz can use to estimate the price per bracelet that will earn her $650 in revenue, we need to set up an equation where the total revenue from selling bracelets is equal to $650.<br /><br />The expression given is $-5p + 115$, which represents the number of bracelets Liz needs to sell. To find the price per bracelet, $p$, that will result in $650 in revenue, we need to set up the equation as follows:<br /><br />$650 = p(-5p + 115)$<br /><br />This equation represents the total revenue ($650) being equal to the price per bracelet ($p) multiplied by the number of bracelets she needs to sell ($-5p + 115).<br /><br />To find the two prices that will earn Liz exactly $650 in revenue, we need to solve the equation $650 = p(-5p + 115)$ for $p$.<br /><br />Expanding the equation, we get:<br />$650 = -5p^2 + 115p$<br /><br />Rearranging the terms, we have:<br />$5p^2 - 115p + 650 = 0$<br /><br />This is a quadratic equation in the form $ax^2 + bx + c = 0$, where $a = 5$, $b = -115$, and $c = 650$.<br /><br />To solve this quadratic equation, we can use the quadratic formula:<br />$p = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$<br /><br />Plugging in the values, we get:<br />$p = \frac{115 \pm \sqrt{(-115)^2 - 4(5)(650)}}{2(5)}$<br /><br />Simplifying further, we have:<br />$p = \frac{115 \pm \sqrt{13225 - 13000}}{10}$<br /><br />$p = \frac{115 \pm \sqrt{225}}{10}$<br /><br />$p = \frac{115 \pm 15}{10}$<br /><br />This gives us two possible solutions for $p$:<br />$p_1 = \frac{115 + 15}{10} = 13$<br />$p_2 = \frac{115 - 15}{10} = 10$<br /><br />Therefore, the two prices that will earn Liz exactly $650 in revenue are $10 and $13.