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Chapter 0: Problem 62

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I find the hardest part in solving a word problem is writing the equation that models the verbal conditions.

Short Answer

Expert verified
Yes, the statement makes sense as writing the equation to model the verbal conditions can indeed be considered the most challenging part of solving word problems in mathematics.

Step by step solution

01

Understanding the Statement

The statement is: 'The hardest part in solving a word problem is writing the equation that models the verbal conditions.'. In broader terms, this statement is expressing an opinion about the difficulty in finding a mathematical representation (equation) for a word problem. Word problems are an integral part of maths where a real-life situation is converted into a mathematical problem.
02

Evaluate the Statement

Now, evaluating whether the statement makes sense or not, one should consider this: Is it generally difficult to model verbal conditions into an equation in word problems? Indeed, in many cases, this could be the most challenging part for students because it requires an understanding of how to convert the language of the problem into a mathematical language. Therefore, it is reasonable to agree that the statement makes sense.
03

Explanation

To further explain why this statement could make sense, consider this: Word problems usually involve several steps like understanding the problem, converting the word problem into mathematical language which includes identifying variables and forming the equation, solving the equation and interpreting the result. Among these, creating a correct mathematically representation often tends to be the part where most errors can occur, especially for those who are new to encountering such problems. Handling variables, figuring out relationships, and forming equations can be complex.
04

Conclusion

In conclusion, the statement that the hardest part in solving a word problem is writing the equation that models the verbal conditions does indeed make sense. This is based on the basis that forming the correct equations from verbal statements can often present the most significant challenges when tackling word problems in mathematics.

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. What's wrong with this argument? Suppose \(x\) and \(y\) represent two real numbers, where \(x>y .\) $$\begin{aligned}2 &>1 \\\2(y-x) &>1(y-x) \\\2 y-2 x &>y-x \\\y-2 x &>-x \\\y &>x\end{aligned}$$ This is a true statement. Multiply both sides by \(y-x\) Use the distributive property. Subtract \(y\) from both sides. Add \(2 x\) to both sides. The final inequality, \(y>x,\) is impossible because we were initially given \(x>y\)

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A city commission has proposed two tax bills. The first bill requires that a homeowner pay \(\$ 1800\) plus \(3 \%\) of the assessed home value in taxes. The second bill requires taxes of \(\$ 200\) plus \(8 \%\) of the assessed home value. What price range of home assessment would make the first bill a better deal?

The formula for converting Fahrenheit temperature, \(F,\) to Celsius temperature, \(C\), is $$C=\frac{5}{9}(F-32)$$ If Celsius temperature ranges from \(15^{\circ}\) to \(35^{\circ},\) inclusive, what is the range for the Fahrenheit temperature? Use interval notation to express this range.

List all numbers that must be excluded from the domain of each rational expression. $$\frac{3}{2 x^{2}+4 x-9}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although \(20 x^{3}\) appears in both \(20 x^{3}+8 x^{2}\) and \(20 x^{3}+10 x\) I'll need to factor \(20 x^{3}\) in different ways to obtain each polynomial's factorization.
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