A fruit stand has to decide what to charge for their produce. They need

Question

\[\$5.30\] for
\[1\] apple and
\[1\] orange. They also need
\[\$7.30\] for
\[1\] apple 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:
Choose 1 answer:
(Choice A) Yes; they should charge
\[\$3.30\] for an apple and
\[\$2.00\] for an orange.
A
Yes; they should charge
\[\$3.30\] for an apple and
\[\$2.00\] for an orange.
(Choice B) Yes; they should charge
\[\$2.00\] for an apple and
\[\$3.30\] for an orange.
B
Yes; they should charge
\[\$2.00\] for an apple and
\[\$3.30\] for an orange.
(Choice C) No; the system has many solutions.
C
No; the system has many solutions.
(Choice D) No; the system has no solution.
D
No; the system has no solution.

Answer 1

To solve for the prices of an apple (let's denote it as \(a\)) and an orange (denote it as \(o\)), we can set up the following system of linear equations based on the information given:

1. From the first statement: \[ a + o = 5.30 \]

2. From the second statement: \[ a + 2o = 7.30 \]

Let's solve this system of equations.

First, we can rewrite the first equation to express \(a\) in terms of \(o\): \[ a = 5.30 - o \]

Now we'll substitute this expression for \(a\) into the second equation: \[ (5.30 - o) + 2o = 7.30 \]

Simplifying this gives: \[ 5.30 - o + 2o = 7.30 \] \[ 5.30 + o = 7.30 \]

Now, solve for \(o\): \[ o = 7.30 - 5.30 = 2.00 \]

Now that we have \(o\), we can substitute it back into the first equation to find \(a\): \[ a + 2.00 = 5.30 \] \[ a = 5.30 - 2.00 = 3.30 \]

Thus, the unique prices found for the apple and orange are:

• Price of an apple \(a = 3.30\)
• Price of an orange \(o = 2.00\)

Therefore, the correct answer is:

(Choice A) Yes; they should charge $3.30 for an apple and $2.00 for an orange.