Think about how to represent the total cost of 8 peaches and 6 nectarines using $p$ and $n$. What expression represents the cost of the peaches? What expression represents the cost of the nectarines? Set their sum equal to $13.20.

Decide which fruit is more expensive. Then, remember: if one quantity is "0.40 less than" another, you subtract $0.40 from the larger one to get the smaller one. Write an equation reflecting that relationship between $p$ and $n$.

For each answer choice, ask: (1) Do the coefficients in the cost equation match 8 peaches and 6 nectarines? (2) Does the relationship equation correctly show the peach price being $0.40 less than the nectarine price?

In Desmos, let $x$ represent $p$ (peach price) and $y$ represent $n$ (nectarine price). You will enter equations using $x$ and $y$ instead of $p$ and $n$.

Type the total cost equation using your chosen variable names, for example: 8x + 6y = 13.20. This line represents all $(x, y)$ pairs where 8 peaches and 6 nectarines cost $13.20.

For each answer choice, convert its first equation to $x$ and $y$ (for example, y = x - 0.40 if it says $n = p - 0.40$) and type it into Desmos. Look at the intersection point of this line with the cost line from step 2, and check whether the coordinates satisfy the story: the $x$-value should be exactly $0.40 less than the $y$-value (peach cheaper than nectarine). Only the correct system will match that condition.

We are told $p$ is the price of one peach (in dollars) and $n$ is the price of one nectarine (in dollars).

The problem gives two separate pieces of information:

• A total cost for a purchase (8 peaches and 6 nectarines cost $13.20).
• A relationship between the prices (a peach is $0.40 less than a nectarine).

Each piece of information will become one equation in the system.

Mason buys 8 peaches at $p$ dollars each and 6 nectarines at $n$ dollars each.

• Cost of peaches: $8p$
• Cost of nectarines: $6n$
• Total cost: $13.20

So the total cost equation is:

Any correct answer must include this equation, and the coefficients (8 and 6) must match the numbers of fruits.

"The price of a peach is $0.40 less than the price of a nectarine" means the nectarine is more expensive.

• Start with the higher price (the nectarine, $n$).
• Subtract $0.40 to get the lower price (the peach, $p$).

So the relationship between the prices is:

This correctly expresses that the peach costs $0.40 less than the nectarine (peach price = nectarine price minus $0.40).

From the total cost and the price relationship, the system of equations is:

Comparing to the answer choices, this system matches choice D:

$p = n - 0.40$
$8p + 6n = 13.20$.