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A fruit stand has to decide what to charge for their produce. They decide to charge $5.30 for 1 apple and 1 orange. They also plan to charge $14 for 2 apples and 2 oranges. We put this information into a system of linear equations. Can we find a unique price for an apple and an orange? Choose 1 answer: (A) Yes; they should charge $3.00 for an apple and $2.30 for an orange. (B) Yes; they should charge $3.00 for an apple and $4.00 for an orange. (c) No; the system has many solutions. (D) No; the system has no solution.

A fruit stand has to decide what to charge for their produce. They decide to charge $5.30 \$ 5.30 for 11 apple and 11 orange. They also plan to charge $14 \$ 14 for 22 apples and 22 oranges. We put this information into a system of linear equations.\newlineCan we find a unique price for an apple and an orange?\newlineChoose 11 answer:\newline(A) Yes; they should charge $3.00 \$ 3.00 for an apple and $2.30 \$ 2.30 for an orange.\newlineB Yes; they should charge $3.00 \$ 3.00 for an apple and $4.00 \$ 4.00 for an orange.\newline(C) No; the system has many solutions.\newline(D) No \mathrm{No} ; the system has no solution.

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Q. A fruit stand has to decide what to charge for their produce. They decide to charge $5.30 \$ 5.30 for 11 apple and 11 orange. They also plan to charge $14 \$ 14 for 22 apples and 22 oranges. We put this information into a system of linear equations.\newlineCan we find a unique price for an apple and an orange?\newlineChoose 11 answer:\newline(A) Yes; they should charge $3.00 \$ 3.00 for an apple and $2.30 \$ 2.30 for an orange.\newlineB Yes; they should charge $3.00 \$ 3.00 for an apple and $4.00 \$ 4.00 for an orange.\newline(C) No; the system has many solutions.\newline(D) No \mathrm{No} ; the system has no solution.
  1. Equations Setup: Let's denote the price of an apple as AA and the price of an orange as OO. We can then write the given information as a system of linear equations:\newline11. For 11 apple and 11 orange, the cost is $5.30\$5.30:\newlineA+O=5.30A + O = 5.30\newline22. For 22 apples and 22 oranges, the cost is $14.00\$14.00:\newline2A+2O=14.002A + 2O = 14.00
  2. Equations Simplification: We can simplify the second equation by dividing every term by 22 to make it easier to compare with the first equation:\newline2A+2O=14.002A + 2O = 14.00\newlineA+O=7.00A + O = 7.00\newlineNow we have two equations:\newline11. A+O=5.30A + O = 5.30\newline22. A+O=7.00A + O = 7.00
  3. Inconsistency Identified: We can see that the two equations are inconsistent with each other because they both describe a relationship between AA and OO, but they give different sums for the same pair of variables. This means that there is no unique solution to this system of equations.
  4. Final Answer: Since the system of equations does not have a unique solution, the correct answer is:\newline(C) No; the system has many solutions.

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