|A hardware store sells three types of shovels, spade, flat, and square. The spade costs $16.00, the flat costs $9.60, and the square costs $12.80 each. The store keeps an inventory of 80 shovels. They always buy twice as many spade shovels as square. One day, after selling out of shovels, the store had receipts totaling $1,072.00. Find how many of each type of shovel were sold that day.|
a. Write a system of equations to represent the information given.
b. Put the system into a matrix. Name the matrix using dimensions.
c. What is the determinant of the coefficients?
d. Use Cramer’s rule to solve the system.
e. If the store doubled all prices and inventory, what would the new matrix be?
The following equations are given:
a. Is it possible to solve for any of the variables using only Equation #1 and Equation #2? Explain your answer. If possible, solve for the variables using only equations #1 and #2.
b. Is it possible to solve for any of the variables using only Equation #1, Equation #2, and Equation #3? Explain your answer. If possible, solve for the variables using only equations #1, #2, and #3.
c. If you found solutions in part b, do these solutions also hold for Equation #4?
3-Danica and Darrelle have developed a lucrative business selling handmade silver bracelets. Darrelle makes the more complex bracelets and Danica makes the simpler ones. It takes Darrelle 4 hours to make 3 bracelets and Danica can make 5 bracelets every 2 hours.
a. Convert this scenario into linear equation(s); show both the standard form and the slope-intercept form of your equation(s).
b. Could any part of this scenario be graphed using any of the special functions discussed in the course text? Explain your answer.
c. Each bracelet Darrelle sells makes $10.50 in profit. Each bracelet Danica sells makes $3.50 in profit. If Darrelle and Danica work the same amount of time, explain each of the steps you will use and then calculate how many hours will it take for the whole business to make at least $500 profit?
4-You are going to go to the grocery store. You have $25 to spend. There are several items on your list that you must purchase and some are “for fun” items that you can purchase if you have enough money.
Your list: 2 gallons of milk for $3.50 each; 2 loaves of bread for $2.75 each; 1 pot roast for $10.45 each.
You want to also purchase some candy bars. The candy is on sale for 43 cents each. Ignore sales tax and answer the following questions.
a. Write an equation representing your shopping experience and use for the number of candy bars.
b. Solve the equation to determine how many candy bars can you purchase?
c. How much change would you have left?