Question

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?

Answer 1

A pound of potato costs $3.10

A dozen egg costs $5.5

A wheel of cheese costs $6.25

Explanation:

Represent

- a dozen egg with D

- a wheel of cheese with W

- a pound of potato with P

For Adam:

`3D + W + 5P = 38.25` ---- (1)

For Barry:

`D + 10P = 36.50` ---- (2)

For Charles:

`2D + 2P = 17.20` ---- (3)

Make D the subject in (2)

`D = 36.50 - 10P`

Substitute 36.50 - 10P for D in (3)

`2(36.50 - 10P) + 2P = 17.20`

`73 - 20P + 2P = 17.20`

`73 - 18P= 17.20`

Collect Like Terms

`- 18P= 17.20 - 73`

`- 18P= -55.8`

`18P= 55.8`

Solve for P

`P = 55.8/18`

`P = 3.1`

Substitute 3.1 for P in
`D = 36.50 - 10P`

`D=36.50 - 10 * 3.1`

`D=36.50 - 31`

`D=5.5`

Substitute 3.1 for P and 5.5 for D in
`3D + W + 5P = 38.25`

`3(5.5) + W + 5(3.1) = 38.25`

`16.5 + W + 15.5 = 38.25`

Solve for W

`W = 38.25 - 16.5 - 15.5`

`W = 6.25`