Two customers purchased the same kind of bread and eggs at a store. The first customer paid 12.45 dollars for

Question

Two customers purchased the same kind of bread and eggs at a store. The first customer paid $12.45$ dollars for $1$ loaf of bread and $2$ dozen eggs. The second customer paid $19.42$ dollars for $4$ loaves of bread and $1$ dozen eggs. What is the cost, in dollars, of $1$ dozen eggs?

A.

$3.77$

B.

$3.88$

C.

$4.15$

D.

$4.34$

Accepted Answer

Choice D is correct. Let l represent the cost, in dollars, of 1 loaf of bread, and let d represent the cost, in dollars, of 1 dozen eggs. It&rsquo;s given that the first customer paid 12.45 dollars for 1 loaf of bread and 2 dozen eggs. Therefore, the first customer&rsquo;s purchase can be represented by the equation l + 2 d = 12.45 . It&rsquo;s also given that the second customer paid 19.42 dollars for 4 loaves of bread and 1 dozen eggs. Therefore, the second customer&rsquo;s purchase can be represented by the equation 4 l + d = 19.42 . The equations l + 2 d = 12.45 and 4 l + d = 19.42 form a system of linear equations, which can be solved by elimination to find the value of d . Multiplying the first equation in the system by - 4 yields - 4 l - 8 d = - 49.8 . Adding - 4 l - 8 d = - 49.8 to the second equation, 4 l + d = 19.42 , yields - 4 l + 4 l + - 8 d + d = - 49.8 + 19.42 , which is equivalent to - 7 d = - 30.38 . Dividing both sides of this equation by - 7 yields d = 4.34 . Therefore, the cost, in dollars, of 1 dozen eggs is 4.34 . Choice A is incorrect. This is the cost, in dollars, of 1 loaf of bread. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.

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