Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Castroville Photography Studio is taking graduation portraits for students at local schools. Eighth graders from Castroville Elementary School ordered 75 basic portrait packages and 89 deluxe portrait packages, for a total of $13,204. The seniors at Weston High ordered 52 basic portrait packages and 98 deluxe portrait packages, for a total of $12,276. How much does each type of package cost? A basic package costs $_____, and a deluxe package costs $_____.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  Castroville Photography Studio is taking graduation portraits for students at local schools. Eighth graders from Castroville Elementary School ordered 75 basic portrait packages and  89 deluxe portrait packages, for a total of $13,204. The seniors at Weston High ordered 52 basic portrait packages and  98 deluxe portrait packages, for a total of $12,276. How much does each type of package cost?  A basic package costs $_____, and a deluxe package costs $_____.

Bytelearn · Accepted Answer

Set Up Equations: Let's denote the cost of a basic package as 'b' and the cost of a deluxe package as 'd'. We need to set up two equations based on the information given. Eighth graders ordered 75 basic and 89 deluxe packages for a total of $13,204. This can be represented by the equation: 75b + 89d = 13,204 Seniors ordered 52 basic and 98 deluxe packages for a total of $12,276. This can be represented by the equation: 52b + 98d = 12,276Elimination Method: We now have a system of equations: 75b + 89d = 13,204 52b + 98d = 12,276 We can use either substitution or elimination to solve this system. Let's use the elimination method to solve for one of the variables.Multiply Equations: To eliminate one of the variables, we can multiply the first equation by 52 and the second equation by 75 to make the coefficients of 'b' the same in both equations. (75b + 89d) * 52 = 13,204 * 52 (52b + 98d) * 75 = 12,276 * 75Subtract Equations: After multiplying, we get the new system of equations: 3900b + 4628d = 686,608 3900b + 7350d = 920,700 Now we can subtract the first equation from the second to eliminate 'b'. (3900b + 7350d) - (3900b + 4628d) = 920,700 - 686,608Solve for d: Subtracting the equations gives us: 3900b + 7350d - 3900b - 4628d = 920,700 - 686,608 2722d = 234,092 Now we can solve for 'd' by dividing both sides by 2722. d = 234,092 / 2722 d = 86Substitute and Solve for b: Now that we have the value of 'd', we can substitute it back into one of the original equations to solve for 'b'. Let's use the first equation: 75b + 89d = 13,204 75b + 89(86) = 13,204 75b + 7654 = 13,204 Now we can solve for 'b' by subtracting 7654 from both sides. 75b = 13,204 - 7654 75b = 5550 b = 5550 / 75 b = 74

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