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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 11,754.TheseniorsatKensingtonHighordered87basicportraitpackagesand58deluxeportraitpackages,foratotalof11,754. 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 ,andadeluxepackagecosts, and a deluxe package costs .Submit

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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 = 11,75458(87B+58D)73=11,754 * 58 (87B + 58D) * 73 = 10,759 * 73

This gives us:

4766B + 4234D = 681,1326341B+4234D=681,132 6341B + 4234D = 785,507

Subtract the first equation from the second:

1575B = $104,375

Solve for B:

B = 104,375/1575=104,375 / 1575 = 66.35

Substitute B = $66.35 into the first equation:

82 * 66.35+73D=66.35 + 73D = 11,754 5436.7+73D=5436.7 + 73D = 11,754 73D = 11,75411,754 - 5436.7 73D = $6317.3

Solve for D:

D = 6317.3/73=6317.3 / 73 = 86.53

So, a basic package costs 66.35,andadeluxepackagecosts66.35, and a deluxe package costs 86.53.

This problem has been solved

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