Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Fairfax Photography Studio is taking graduation portraits for students at local schools. Eighth graders from Fairfax Elementary School ordered 82 basic portrait packages and 73 deluxe portrait packages, for a total of $11,754. The seniors at Kensington High ordered 87 basic portrait packages and 58 deluxe portrait packages, for a total of $10,759. How much does each type of package cost?A basic package costs $, and a deluxe package costs $.Submit
Question
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Fairfax Photography Studio is taking graduation portraits for students at local schools. Eighth graders from Fairfax Elementary School ordered 82 basic portrait packages and 73 deluxe portrait packages, for a total of 10,759. How much does each type of package cost?A basic package costs .Submit
Solution
Let's denote the cost of a basic package as B and the cost of a deluxe package as D.
From the information given, we can form two equations:
For Fairfax Elementary School: 82B + 73D = $11,754
For Kensington High: 87B + 58D = $10,759
This is a system of linear equations that we can solve using the elimination method.
First, we can multiply the first equation by 58 and the second equation by 73 to allow the D terms to cancel out when subtracted:
(82B + 73D) * 58 = 10,759 * 73
This gives us:
4766B + 4234D = 785,507
Subtract the first equation from the second:
1575B = $104,375
Solve for B:
B = 66.35
Substitute B = $66.35 into the first equation:
82 * 11,754 11,754 73D = 5436.7 73D = $6317.3
Solve for D:
D = 86.53
So, a basic package costs 86.53.
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