You are a music store manager and you are trying to decide how many CDs and vinyl records to order for a new release from a popular artist. The CDs cost $10 each and the vinyl records cost $15 each. You need a total of 50 items to stock and you have a budget of $600. Write a system of equations to represent this scenario and solve for the number of CDs and vinyl records to order.
Let x represent the number of CDs and y represent the number of vinyl records.
Equation 1: x + y = 50 (total number of items)
Equation 2: 10x + 15y = 600 (total cost)
Solving the system of equations:
Equation 1: x + y = 50
Equation 2: 10x + 15y = 600
Multiply Equation 1 by 10:
10x + 10y = 500
Subtract the modified Equation 1 from Equation 2:
10x + 15y - 10x - 10y = 600 - 500
5y = 100
y = 20
Substitute y = 20 into Equation 1:
x + 20 = 50
x = 30
Therefore, the manager should order 30 CDs and 20 vinyl records to have a total of 50 items in stock and stay within the budget.
maqke this like a 8th grader wrote it
Let x be the CDs and y be the vinyl records.
x + y = 50 (total items)
10x + 15y = 600 (total cost)
To solve:
x + y = 50
10x + 15y = 600
Multiply the first equation by 10:
10x + 10y = 500
Subtract the multiplied first equation from the second equation:
10x + 15y - 10x - 10y = 600 - 500
5y = 100
y = 20
So, the manager should order 30 CDs and 20 vinyl records.