Answered

Rebeca bought jeans, shirts, and shoes at a clothing store. The expression 2(40 + 25) + 60 represents the total cost of the items she bought. Which best interprets and evaluates the numerical expression?


AThe value of the numerical expression is $330 because Rebeca bought 2 pairs of jeans, 1 shirt, and 1 pair of shoes.
BThe value of the numerical expression is $190 because Rebeca bought 2 pairs of jeans, 2 shirts, and 1 pair of shoes.
CThe value of the numerical expression is $190 because Rebeca bought 1 pair of jeans, 2 shirts, and 1 pair of shoes.
DThe value of the numerical expression is $330 because Rebeca bought 2 pairs of jeans, 2 shirts, and 1 pair of shoes.

Verified Answer :

  • Evaluate the expression using the order of operations: \(2(40 + 25) + 60 = 2(65) + 60 = 130 + 60 = 190\).
  • Apply the distributive property to interpret the items: \(2 \times 40 + 2 \times 25 + 60\), which represents 2 items at \(\$40\), 2 items at \(\$25\), and 1 item at \(\$60\).
  • Compare the calculated total and the item breakdown with the given options to find the match.
  • The correct choice is B, with a total cost of \(\boxed{\$190}\).

Explanation

  1. Evaluating the Numerical Expression

The numerical expression \(2(40 + 25) + 60\) represents the total cost of clothes purchased by Rebeca. To evaluate this, we use the order of operations, specifically addressing the parentheses first. Adding the values inside the parentheses gives \(40 + 25 = 65\). Then, multiplying this sum by 2 results in \(2 \times 65 = 130\). Adding the final 60 gives a total of \(130 + 60 = 190\). Therefore, the total cost of the items is \(\$190\).

  1. Interpreting the Items Purchased

To interpret the expression, we apply the distributive property: \(2(40 + 25) + 60 = 2 \times 40 + 2 \times 25 + 60\). This expansion clarifies that Rebeca bought two items at \(\$40\) each, two items at \(\$25\) each, and one item at \(\$60\). Comparing this with the provided options, Option B states that the value is \(\$190\) and Rebeca bought 2 pairs of jeans, 2 shirts, and 1 pair of shoes. Assigning the prices appropriately (jeans at \(\$40\), shirts at \(\$25\), and shoes at \(\$60\)), we see that \(2 \times 40 + 2 \times 25 + 60 = 80 + 50 + 60 = 190\). Thus, Option B is the correct interpretation.

Examples

Understanding numerical expressions is essential for managing personal budgets and shopping. For example, if you know the prices of individual groceries and the quantities you intend to buy, you can represent the total cost as an algebraic expression to predict your final bill. This skill helps in planning expenses, comparing prices between stores, and ensuring you have enough money before heading to the checkout counter.

Related Questions