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Adam, Barry, and Charles visited a small farmers market last Saturday. Adam purchased 3 dozen eggs, 1 wheel of cheese, and 5 pounds of potatoes. Barry bought 1 dozen eggs and 10 pounds of potatoes, while Charles purchased 2 dozen eggs and 2 pounds of potatoes. If Adam's bill was $38.25, Barry's $36.50 and Charles' $17.20, how much did a dozen eggs, a wheel of cheese and a pound of potatoes cost?

Respuesta :

MrRoyal

Answer:

A pound of potato costs $3.10

A dozen egg costs $5.5

A wheel of cheese costs $6.25

Step-by-step explanation:

Represent

- a dozen egg with D

- a wheel of cheese with W

- a pound of potato with P

For Adam:

[tex]3D + W + 5P = 38.25[/tex] ---- (1)

For Barry:

[tex]D + 10P = 36.50[/tex] ---- (2)

For Charles:

[tex]2D + 2P = 17.20[/tex] ---- (3)

Make D the subject in (2)

[tex]D = 36.50 - 10P[/tex]

Substitute 36.50 - 10P for D in (3)

[tex]2(36.50 - 10P) + 2P = 17.20[/tex]

[tex]73 - 20P + 2P = 17.20[/tex]

[tex]73 - 18P= 17.20[/tex]

Collect Like Terms

[tex]- 18P= 17.20 - 73[/tex]

[tex]- 18P= -55.8[/tex]

[tex]18P= 55.8[/tex]

Solve for P

[tex]P = 55.8/18[/tex]

[tex]P = 3.1[/tex]

Substitute 3.1 for P in [tex]D = 36.50 - 10P[/tex]

[tex]D=36.50 - 10 * 3.1[/tex]

[tex]D=36.50 - 31[/tex]

[tex]D=5.5[/tex]

Substitute 3.1 for P and 5.5 for D in [tex]3D + W + 5P = 38.25[/tex]

[tex]3(5.5) + W + 5(3.1) = 38.25[/tex]

[tex]16.5 + W + 15.5 = 38.25[/tex]

Solve for W

[tex]W = 38.25 - 16.5 - 15.5[/tex]

[tex]W = 6.25[/tex]

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