Question

04.03 MC) The price of blackberries at a farm is $1.56 per pound. Which equation can be used to determine c, the total price of n pounds of blackberries? (5 points) Select one:

A. c = 1.56n
B. c= 1.56 over n
C. c = 1.56 + n
D. c = 1.56 − n

Answer 1

The equation that represents the relationship between the total price and the pounds of blackberries purchased is c = 1.56n.

Explanation:

We are given that the price of the blackberries is $1.56 per pound. Therefore, for each pound, the price increases by $1.56.

This is going to be a linear relationship, so our equation is going to be in the form of
`y = mx + b` (this is the parent function for a linear function).

For example, say an individual purchases 3 pounds of blackberries.

Therefore, the initial purchase is going to start at $0 (nothing has been paid for if no blackberries are purchased).

Then, we will have to add the price to itself three times to get our total payment:
`1.56+1.56+1.56 = \$4.68`

After we do this, we can realize that when we add the same value a certain number of times, we can just multiply that value by the amount of times we've added it.

If we purchase the 3 pounds of blackberries, we would multiply $1.56 by 3 to get the total price of the blackberries. So, if we label our pounds of blackberries with a variable, we can see this relationship.

Now, our three pounds of blackberries can be labeled as n. So, we are multiplying $1.56 by n.

`\$1.56 * n`

This would give us our total cost, c.

Therefore, our multiplication of $1.56 and n is equal to c, so we can set those equal to each other.

`c=\$1.56* n`

Finally, in math, there is a statement that says that when you multiply a constant by a variable, you can drop the multiplication symbol and simply combine the two (for example,
`3 * n` becomes
`3n`). With this, our equation now becomes:

`c= \$1.56n`

Therefore, our answer is Choice A.

Answer 2

A. c = 1.56n

Explanation:

In this situation n equals the independent variable. The independent variable means that no matter what the rest of the equation is this will be equal to a certain number.

Now, the correct answer will be A. This is because you will want to multiply 1.56 per pound. When you have a situation like this you know that the amount of money will be added to itself over and over depending on the independent variable. In other words, it will be multiplied by the independent variable.

Lets use this formula:

`x * y = z`

x = Price of blackberries

y = Number of pounds

z = Total price of blackberries per y pounds.

Now change that to have our variables:

`1.56* n = c`

or in other words:

`c = 1.56n`

In the table below I will provide an example of what c will look like depending on n.

`\begin{array}c \cline{1-2} \textbf{n} & \textbf{c} \\ \cline{1-2} 0 & 0 \\ \cline{1-2} 1 & 1.56 \\ \cline{1-2} 2 & 2.13 \\ \cline{1-2} 3 & 4.68 \\ \cline{1-2} 4 & 6.24 \\ \cline{1-2} 5 & 7.80 \\ \cline{1-2} \end{array}`

As you can see, n will be multiplied by 1.56 to find c. Thus proving our answer is A.
`c = 1.56n`

~Hope this helped!