Answered

Fuji apples cost $\$3.00$ per pound, and Golden Delicious apples cost $\$2.00$ per pound. A childcare center purchases 30 pounds of a combination of the two types of apples for a total of $\$80$.



\begin{table}

\captionsetup{labelformat=empty}

\caption{Apples}


PoundsCost per PoundTotal

Fuji		$30-g$3$x$

Golden Delicious		$g$2

Total		3080




\end{table}



Which value could replace $x$ in the table?


A$30-g+g$
B$3(30-g)$
C$30-g(3)$
D$30-g+3$

Verified Answer :

  • To find the total cost of the Fuji apples, multiply their weight by their cost per pound.
  • The weight of the Fuji apples is given as \(30-g\) pounds and their cost is \(\$3.00\) per pound.
  • Multiplying these gives the total cost: \(x = 3(30-g)\).
  • Therefore, the correct expression representing \(x\) is \(\boxed{3(30-g)}\).

Explanation

  1. Analyzing the Table and Calculating Total Cost

The problem asks us to determine the expression that represents the total cost of Fuji apples, denoted by \(x\) in the provided table. We are given the following information:

  • The Fuji apples weigh \(30-g\) pounds.
  • The cost of Fuji apples is \(\$3.00\) per pound.
  • The total cost \(x\) is obtained by multiplying the weight of the apples by their cost per pound.

We use the standard formula for total cost, which is:
\[\text{Total Cost} = \text{Weight} \times \text{Cost per unit weight}\]
Substituting the given values for the Fuji apples, we have:
\[x = (30-g) \times 3\]
This can be rewritten as:
\[x = 3(30-g)\]
Thus, the correct expression for \(x\) is \(3(30-g)\).

Examples

This problem illustrates how to organize data into tables to solve systems of linear equations. In real life, similar tables are used in budgeting and inventory management to calculate expenses. For example, if you are planning to buy two different types of supplies, say notebooks and pens, you can use a table to keep track of the quantity of each, their individual costs, and the total cost for each category to ensure you stay within your budget. By setting up the total cost as the product of the quantity and unit price, you can easily derive equations that help you solve for the number of items to purchase.

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