Problem 127 - Beginning and Intermediate Algebra

Question

Solve each problem. Nadine enjoys playing Triominoes every Wednesday night. Last Wednesday, on four successive turns, her scores were $$ \begin{array}{lllll} -19, & 28, & -5, & \text { and } & 13 . \end{array} $$ What was her final score for the four turns?

Step-by-Step Solution

Answer

Nadine's final score is 17.

Step 1 - Identify the given scores

In this exercise, the scores given for Nadine's four successive turns are: \(-19\), 28, \(-5\), and 13.

Step 2 - Sum the scores

To determine Nadine's final score, sum the values of all her turns. Calculate: \[ -19 + 28 - 5 + 13 \]

Step 3 - Calculate the sum

Perform the addition and subtraction in sequence: \(-19 + 28 = 9\) \(9 - 5 = 4\) \(4 + 13 = 17\)

Step 4 - State the final score

Nadine's final score after the four turns is 17.

Key Concepts

math problem solving

Learning how to solve math problems involves understanding the procedures and concepts behind them. Let's break down a simple exercise using integer addition and subtraction. Nadine's scores in her game are: \( -19, 28, -5, \text{ and } 13. \). To find her final score, we need to add these integers together. This involves:

• Identifying each score
• Summing them step by step
• Simplifying the result

Being systematic in problem-solving helps to ensure accuracy and builds a strong foundational skill for more complex problems.

integer operations

Integer operations include addition, subtraction, multiplication, and division of whole numbers. In this exercise, we focus on integer addition and subtraction. Here’s how you do it:

• When adding a positive integer to a negative one, subtract the smaller number from the larger one and use the sign of the larger number.
• When two negative numbers are added, add them like positive numbers, then add a negative sign.
• Subtraction of integers is like adding a negative.

For instance, Nadine's scores are \( -19, 28, -5, \text{ and } 13. \). Let's add them step-by-step: \( -19 + 28 = 9 \). Next, subtract: \( 9 - 5 = 4 \). Finally, add: \( 4 + 13 = 17. \) Using these rules, Nadine's final score is 17.

basic arithmetic

Basic arithmetic consists of straightforward operations with numbers, including addition, subtraction, multiplication, and division. For Nadine’s game, we used addition and subtraction:

• Addition combines values to find the total.
• Subtraction finds the difference by taking one value away from another.

When performing these operations:

Start with a clear understanding of which numbers you are dealing with. For Nadine’s score calculation:

• Add the positive and negative integers carefully.
• Follow the operations in sequence.
• Double-check your work.

Therefore, \( -19 + 28 = 9 \), \( 9 - 5 = 4 \), \( 4 + 13 = 17 \). Nadine's final score, after performing these basic operations, is 17.