AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Denise has a home-based business making and selling scented soaps. She intially spent to purchase soap-making equipment, and the materials for each pound of soap cost . Denise sells the soap for per pound. Eventually, she will sell enough soap to cover the cost of the equipment. How much soap will that be? What will be Denise's total sales and costs be?Once Denise sells _____ pounds of soap, her sales and costs will both be _____.
Full solution
Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Denise has a home-based business making and selling scented soaps. She intially spent to purchase soap-making equipment, and the materials for each pound of soap cost . Denise sells the soap for per pound. Eventually, she will sell enough soap to cover the cost of the equipment. How much soap will that be? What will be Denise's total sales and costs be?Once Denise sells _____ pounds of soap, her sales and costs will both be _____.
- Define Variables: Let's define the variables:Let be the number of pounds of soap Denise sells.Denise's total cost () for making pounds of soap includes the initial equipment cost and the cost of materials per pound.Denise's total sales () come from selling the soap at a certain price per pound.We can write two equations to represent the total cost and total sales:Total cost equation: Total sales equation:
- Write Equations with Given Numbers: Now let's write the equations with the given numbers:Initial cost = Cost per pound = Price per pound =
- Find Break-Even Point: Denise will break even when her total sales equal her total costs. So we set the cost equation equal to the sales equation to find the break-even point:
- Solve for x: Now we solve for x:Denise needs to sell pounds of soap to cover her initial costs.
- Calculate Total Sales and Costs: To find the total sales and costs when Denise sells pounds of soap, we substitute into the sales equation:So Denise's total sales and costs will both be when she sells pounds of soap.
