Chapter 2: Problem 27
A farmer purchases \(200 \mathrm{lbs}\). of feed each month to support 35 cows. How much total feed (in lbs.) will he need per month, at this rate, if he acquires an additional 245 cows? A. 43 B. 243 C. 1,400 D. 1,600
Short Answer
Expert verified
The farmer will need 1,600 lbs. of feed per month to support the new total number of cows.
Step by step solution
01
Calculate the rate of feed consumption per cow
First, we need to find how much feed is consumed by one cow in a month. To do this, we will divide the total amount of feed by the number of cows.
Rate of feed consumption per cow = \( \frac{Total \ feed \ consumed}{Number \ of \ cows} \)
Rate of feed consumption per cow = \( \frac{200}{35} \)
02
Calculate the total number of cows
Next, we need to find the total number of cows after the farmer acquires an additional 245 cows. To do this, we add the initial number of cows to the additional number of cows.
Total number of cows = Initial number of cows + Additional cows
Total number of cows = 35 + 245
03
Calculate the total amount of feed required
Finally, to find the total amount of feed required for the total number of cows per month, we will multiply the rate of feed consumption per cow with the total number of cows.
Total feed required = Rate of feed consumption per cow * Total number of cows
Total feed required = \( \frac{200}{35} \) * (35 + 245)
04
Simplify and choose the correct answer
Simplify the equation and find the correct option from the given choices.
Total feed required = \( \frac{200}{35} \) * 280
Total feed required = 1,600
The correct answer is option D. 1,600 lbs. of feed will be required per month to support the new total number of cows.
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with Vaia!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Mathematical Reasoning
Mathematical reasoning involves the capacity to think logically about numbers and mathematical concepts to solve problems. It's essential for tackling various types of mathematical questions, including those on the General Educational Development (GED) test. It requires understanding and applying quantitative relationships in diverse contexts, presenting one's reasoning, and critiquing the reasoning of others.
Using mathematical reasoning, we start by identifying what we know and what we need to find out. For example, in the given exercise, we know the monthly feed consumption for a particular number of cows. The goal is to determine the increased feed required when more cows are added. Reasoning mathematically allows us to break down the problem into smaller parts, understand the relationship between the parts, and apply mathematical operations to reach a solution.
Using mathematical reasoning, we start by identifying what we know and what we need to find out. For example, in the given exercise, we know the monthly feed consumption for a particular number of cows. The goal is to determine the increased feed required when more cows are added. Reasoning mathematically allows us to break down the problem into smaller parts, understand the relationship between the parts, and apply mathematical operations to reach a solution.
Rate Problems
Rate problems are a type of word problem that involve the comparison of different quantities and how one quantity changes in relation to another. Commonly, rate problems require dividing one quantity by another to find the rate of change or consumption.
As seen in our exercise, we calculate the feed consumption per cow by dividing the total amount of feed by the number of cows to find the rate. This approach translates a real-world scenario into a mathematical one and is critical for soling rate problems. In daily life, rate problems appear in various forms, such as calculating the speed of a vehicle (distance per hour) or the efficiency of a machine (output per minute). Mastering rate problems is a skill that proves useful both academically and in practical situations.
As seen in our exercise, we calculate the feed consumption per cow by dividing the total amount of feed by the number of cows to find the rate. This approach translates a real-world scenario into a mathematical one and is critical for soling rate problems. In daily life, rate problems appear in various forms, such as calculating the speed of a vehicle (distance per hour) or the efficiency of a machine (output per minute). Mastering rate problems is a skill that proves useful both academically and in practical situations.
GED Test Preparation
Preparing for the GED test involves developing skills in a range of subjects, including Mathematical Reasoning. This section of the test assesses problem-solving abilities, understanding of mathematical concepts, and capacity to work with numbers and algebra. To excel, students need to practice different types of math problems, including word problems, rate problems, algebra, and geometry.
Using exercises like the one provided helps to practice and build confidence. Approaching GED test preparation systematically by breaking down complex problems into understandable steps can make solving them manageable. It is also important to familiarize oneself with the test format and question types, manage time effectively during the test, and utilize resources such as textbooks, online courses, and GED practice tests.
Using exercises like the one provided helps to practice and build confidence. Approaching GED test preparation systematically by breaking down complex problems into understandable steps can make solving them manageable. It is also important to familiarize oneself with the test format and question types, manage time effectively during the test, and utilize resources such as textbooks, online courses, and GED practice tests.
Word Problems Math
Word problems in math require translating a written statement into a mathematical equation to find a solution. They blend real-life situations with mathematical abstractions and often involve several steps or operations to solve.
The key to solving word problems is first to understand the scenario described. Identifying the quantities involved and the question asked goes a long way. Then, translating this verbal description into numerical expressions or equations is the next big step. For example, in the GED test math problem provided, translating the number of cows and the amount of feed into an equation allowed us to calculate the required feed. Practice is essential in mastering word problems, as they are a staple in math education from elementary school through college preparatory exams like the GED.
The key to solving word problems is first to understand the scenario described. Identifying the quantities involved and the question asked goes a long way. Then, translating this verbal description into numerical expressions or equations is the next big step. For example, in the GED test math problem provided, translating the number of cows and the amount of feed into an equation allowed us to calculate the required feed. Practice is essential in mastering word problems, as they are a staple in math education from elementary school through college preparatory exams like the GED.