Problem 37 - Basic College Mathematics

Question

Bryce delivers car parts to auto service centers. On Thursday he had 15 deliveries scheduled. By noon he had delivered only 4 orders. What is the ratio of: a) orders delivered to total number of orders? b) orders delivered to orders not delivered? c) orders not delivered to total number of orders?

Step-by-Step Solution

Answer

a) 4/15, b) 4/11, c) 11/15

Step 1 - Identify Given Values

Identify the total number of orders and the number of orders delivered by noon. Total orders = 15, Orders delivered = 4.

Step 2 - Calculate Orders Not Delivered

Calculate the number of orders that were not delivered by subtracting the number of delivered orders from the total orders. Orders not delivered = 15 - 4 = 11.

Step 3 - Calculate Ratio of Orders Delivered to Total Orders

The ratio of orders delivered to total orders is calculated by dividing the number of orders delivered by the total number of orders. Ratio = 4/15.

Step 4 - Calculate Ratio of Orders Delivered to Orders Not Delivered

The ratio of orders delivered to orders not delivered is calculated by dividing the number of orders delivered by the number of orders not delivered. Ratio = 4/11.

Step 5 - Calculate Ratio of Orders Not Delivered to Total Orders

The ratio of orders not delivered to total orders is calculated by dividing the number of orders not delivered by the total number of orders. Ratio = 11/15.

Key Concepts

Understanding Ratios

A ratio is a way to compare two or more quantities. It's like saying how much of one thing there is compared to another thing. For example, if you have 4 apples and 6 oranges, the ratio of apples to oranges is 4:6. We often simplify ratios by dividing both parts by the same number, like simplifying 4:6 to 2:3.

In our original exercise, we looked at orders Bryce delivered and orders he didn't deliver. Let's break that down:

• Orders delivered: 4
• Total orders: 15
• Orders not delivered: 11

We calculated the following ratios:

• Orders delivered to total orders: 4/15
• Orders delivered to orders not delivered: 4/11
• Orders not delivered to total orders: 11/15

By comparing these quantities using ratios, we gain a deeper understanding of the data.

Basic Algebra in Ratios

Algebra is a branch of mathematics where we use symbols and letters to represent numbers and quantities in formulas and equations. Understanding how to work with ratios is foundational in algebra.

In our problem, we used basic algebraic operations like addition and subtraction to find the values we needed for the ratios. For example:

• Calculating orders not delivered: Total orders - Orders delivered = Orders not delivered 15 - 4 = 11

We then divided these numbers to find the ratios:

• Ratio of orders delivered to total orders: 4/15
• Ratio of orders delivered to orders not delivered: 4/11
• Ratio of orders not delivered to total orders: 11/15

Mastering these basic calculations helps you solve more complex algebraic problems in the future.

Problem-Solving Techniques

Problem-solving is about breaking down a problem into manageable steps and solving it one piece at a time. This exercise showed a great example of that.

We followed a step-by-step method:

• Identify the given values: Total orders and orders delivered.
• Calculate missing values: Orders not delivered.
• Formulate the ratios: Orders delivered to total orders, orders delivered to orders not delivered, orders not delivered to total orders.

Here are some useful problem-solving tips:

• Read the problem carefully to understand what is asked.
• Identify and list out all the given information.
• Use basic operations to find any missing values.
• Check your work to make sure the ratios make sense and are properly simplified.

By practicing these techniques, you can improve your problem-solving skills and tackle more challenging questions with confidence.