Two families are saving up for a summer trip. The Smith family originally has $1,000 and will save $50 every week. The Jones family originally has $500 and will save $75 every week. After how many weeks will the two families have saved up the same amount of money?

Use the system of three equations in three variables to solve each problem. Work schedules A college student earns 198.50 per week working three part-time jobs. Half of his 30-hour work week is spent cooking hamburgers at a fast-food chain, earning 5.70 per hour. In addition, the student earns 6.30 per hour doing janitorial work. How many hours per week does the student work at each job

How can you tell when a system of three linear equations with three variables has no solution? Infinitely many solutions?

Motherboards A manufacturer produces motherboards and chips for computers. The production line produces 45 items per day, and each motherboard requires two chips the northbridge and the southbridge. a. Using M for the number of motherboards and C for the number of chips, write a system of two equation in two unknowns that determines the number of motherboards and the number of chips that are produced each day. b. How many motherboards and how many chips are produced each day?

Translate to a system of equations and solve: Greta wants to make 5 pounds of a nut mix using peanuts and cashews. Her budget requires the mixture to cost her $6 per pound. Peanuts are $4 per pound and cashews are $9 per pound. How many pounds of peanuts and how many pounds of cashews should she use?

Translate to a system of equations and then solve: Erin spent 30 minutes on the rowing machine and 20 minutes lifting weights at the gym and burned 430 calories. During her next visit to the gym she spent 50 minutes on the rowing machine and 10 minutes lifting weights and burned 600 calories. How many calories did she burn for each minutes on the rowing machine? How many calories did she burn for each minute of weight lifting?

Translate to a system of equations and solve: Sammy has most of the ingredients he needs to make a large batch of chili. The only items he lacks are beans and ground beef. He needs a total of 20 pounds combined of beans and ground beef and has a budget of $3 per pound. The price of beans is $1 per pound and the price of ground beef is $5 per pound. How many pounds of beans and how many pounds of ground beef should he purchase?

The number of sides x and the combined number of sides and diagonals y for each of three regular polygons are shown below. Write a system of linear equations to find an equation of the form y=ax2+bx+c that represents the relationship between x and y for the three polygons.