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? 650=p(-5p+115) 650p=p(-5p+115) What two prices will earn Liz exactly 650 in revenue? or

To find the equation that Liz can use to estimate the price per bracelet that will earn her $$650 in revenue, we need to set up an equation where the total revenue is equal to$$ 650.

The total revenue can be calculated by multiplying the number of bracelets sold by the price per bracelet. In this case, the number of bracelets sold is given by the expression $$-5p+115$$ .

So, the equation that represents the total revenue is:

$$650 = p(-5p+115)$$

Now, let's solve this equation to find the two prices that will earn Liz exactly $$650 in revenue. First, let's expand the equation:$$ 650 = -5p^2 + 115p $$Next, let's rearrange the equation to set it equal to zero:$$ -5p^2 + 115p - 650 = 0 $$Now, we can solve this quadratic equation using the quadratic formula:$$ p = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$In this case,$$ a = -5 $$,$$ b = 115 $$, and$$ c = -650 $$. Plugging these values into the quadratic formula, we get:$$ p = \frac{-115 \pm \sqrt{115^2 - 4(-5)(-650)}}{2(-5)} $$Simplifying further:$$ p = \frac{-115 \pm \sqrt{13225 - 13000}}{-10}p = \frac{-115 \pm \sqrt{225}}{-10}p = \frac{-115 \pm 15}{-10} $$Now, we have two possible solutions for$$ p $$:$$ p_1 = \frac{-115 + 15}{-10} = \frac{-100}{-10} = 10p_2 = \frac{-115 - 15}{-10} = \frac{-130}{-10} = 13 $$Therefore, the two prices that will earn Liz exactly$$ 650 in revenue are $$10 and$$ 13.