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:

Dozen eggs = $5.5

Wheel of cheese = $6.25

Pound of potatoes = $3.1

Step-by-step explanation:

Let the cost

Dozen of egg = x

Wheel of cheese = y

Pound of potato = z

We will form linear equations using the information given in the question

Adam purchased 3 dozen eggs, 1 wheel of cheese, and 5 pounds of potatoes

3x + y + 5z = 38.25 ................(1)

Barry bought 1 dozen eggs and 10 pounds of potatoes

x + 10z = 36.50 ............(2)

Charles purchased 2 dozen eggs and 2 pounds of potatoes

2x + 2z = 17.20  .................(3)

solving 2 and 3

x = $5.5  and z = $3.1

substitute these values in equation 1

we get

y = $6.25

The cost

Dozen eggs = $5.5

Wheel of cheese = $6.25

Pound of potatoes = $3.1

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