Mack's Knick-Knacks is having a clearance sale on costume jewelry sets next week. The manager wants to find how much to charge per set in order to sell $100 worth. Based on previous clearance events, the manager knows he can use the expression –7p+75 to find the number of sets he will sell based on a set's price, p.Which equation can the manager use to find the price per set needed to sell $100 worth?100=p(–7p+75)100p=p(–7p+75)To the nearest dollar, what is the highest price the manager can use to sell $100 worth of costume jewelry sets?$Submit
Question
Mack's Knick-Knacks is having a clearance sale on costume jewelry sets next week. The manager wants to find how much to charge per set in order to sell 100 worth?100=p(–7p+75)100p=p(–7p+75)To the nearest dollar, what is the highest price the manager can use to sell Submit
Solution
The manager can use the equation 100 = p(-7p + 75) to find the price per set needed to sell 100, the manager can solve for p to find the price per set.
To solve for p, we can follow these steps:
- Distribute p to both terms inside the parentheses: 100 = -7p^2 + 75p
- Rearrange the equation to set it equal to zero: 7p^2 - 75p + 100 = 0
- This is a quadratic equation in the form of ax^2 + bx + c = 0. We can solve for p using the quadratic formula, p = [-b ± sqrt(b^2 - 4ac)] / (2a). Here, a = 7, b = -75, and c = 100.
- Substituting these values into the quadratic formula gives us two possible solutions for p.
After calculating, we find that the two possible prices are approximately 1.59. Since the question asks for the highest price, the manager can charge approximately 100 worth of costume jewelry sets.
Similar Questions
An article is marked up by P% above the cost price. If shopkeeper offers discount of 25% and still earns a profit of 35%. For earning a profit of 71%, how much discount should be offered by shopkeeper?
Josh's club at school is selling suckers for a fundraiser. They sold the suckers for $.50$.50 a piece but had to pay a shipping cost of $30$30. The function for their sucker sales is P(s)=.50s−30𝑃(𝑠)=.50𝑠−30, where s𝑠 is the number of suckers sold and P𝑃 represents the profit made. If they sold 150150 suckers, how much profit would they make? Josh's club would make $$ Answer 1 Question 20 for selling 150150 suckers.
The booster club at Preston Hills High School is selling tickets to a fundraiser for the marching band. The club wants to figure out how much to charge per ticket to make $3,600, which is the total cost for six new trumpets. Based on previous fundraisers, the expression –4p+260 can be used to estimate the number of tickets the booster club will sell given the ticket price, p.Which equation can the booster club use to estimate a ticket price that will raise $3,600 in revenue?3,600p=p(–4p+260)3,600=p(–4p+260)What is the lowest ticket price the booster club can use to make $3,600 in revenue?
Sam goes to Paw-fect Pets to buy his dog a toy and some food. If he buys a chew toy for $16, he'll have exactly enough money left over to buy 7 cans of dog food. Alternatively, if he buys a ball for $3.50, he'll have exactly enough left over to buy 12 cans of dog food.Which equation can you use to find p, the price of a can of dog food?16–7p=3.5–12p16+7p=3.5+12pWhat is the price of a can of dog food?$
John owns a hotdog stand. His profit is represented by with P(x) being profit and x the number of hotdogs sold. What is the most he can earn?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.