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The employees of a hardware store ordered lunch from a local delicatessen. The lunch consisted of 4 turkey sandwiches and 7 orders of french fries, for a total cost of $38.30. The next day, the employees ordered 5 turkey sandwiches and 5 orders of french fries totaling $40.75. What does the delicatessen charge for a turkey sandwich? What is the charge for an order of french fries?

Respuesta :

MrRoyal

Answer:

Charges of Turkey is $6.25

Charges of French Fries is $1.90

Step-by-step explanation:

Given

Represent Turkeys with T and French Fries with F;

[tex]4T + 7F = 38.3[/tex]

[tex]5T + 5F = 40.75[/tex]

Required

Determine the values of T and F

[tex]5T + 5F = 40.75[/tex]

Divide through by 5

[tex]T + F = 8.15[/tex]

Make F the subject

[tex]F = 8.15 - T[/tex]

Substitute 8.15 - T for F in the first equation

[tex]4T + 7F = 38.3[/tex]

[tex]4T + 7(8.15 - T) = 38.30[/tex]

[tex]4T + 57.05 - 7T = 38.30[/tex]

Collect Like Terms

[tex]4T - 7T = 38.30 - 57.05[/tex]

[tex]-3T = -18.75[/tex]

Solve for T

[tex]T = -18.75/-3[/tex]

[tex]T = 6.25[/tex]

Recall that:

[tex]F = 8.15 - T[/tex]

[tex]F = 8.15 - 6.25[/tex]

[tex]F = 1.90[/tex]

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