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

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:

$3D + W + 5P = 38.25$ ---- (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

$W = 38.25 - 16.5 - 15.5$

$W = 6.25$