Which of the following describes the equation x - 11 = 44?
Understand the Problem
This question asks us to determine which of sentences below accurately describes the equation x - 11 = 44.
Answer
Rachel is $x$ years old. Alonzo is 11 years younger than Rachel. Alonzo is 44 years old.
Answer for screen readers
Rachel is $x$ years old. Alonzo is 11 years younger than Rachel. Alonzo is 44 years old.
Steps to Solve
- Analyze the first sentence
The first sentence states: "Rachel is $x$ years old. Alonzo is 11 years younger than Rachel. Alonzo is 44 years old." This translates to: Rachel's age: $x$ Alonzo's age: $x - 11$ Alonzo's age: $44$ So, $x - 11 = 44$. This matches the given equation.
- Analyze the second sentence
The second sentence states: "Alonzo is $x$ years old. Rachel is 11 years older than Alonzo. Rachel is 44 years old." This translates to: Alonzo's age: $x$ Rachel's age: $x + 11$ Rachel's age: $44$ So, $x + 11 = 44$. This does NOT match the given equation.
- Analyze the third sentence
The third sentence states: "Rachel is $x$ years old. In 11 more years, she will be 44 years old." This translates to: Rachel's age: $x$ Rachel's age in 11 years: $x + 11$ Rachel's age in 11 years: $44$ So, $x + 11 = 44$. This does NOT match the given equation.
- Analyze the fourth sentence
The fourth sentence states: "Alonzo is $x$ years old. And 11 years ago, he was 44 years old." This translates to: Alonzo's age: $x$ Alonzo's age 11 years ago: $x - 11$ Alonzo's age 11 years ago: $44$ So, $x - 11 = 44$. This matches the given equation.
- Determine the correct answer
The first sentence, "Rachel is $x$ years old. Alonzo is 11 years younger than Rachel. Alonzo is 44 years old," correctly describes the equation $x - 11 = 44$.
Rachel is $x$ years old. Alonzo is 11 years younger than Rachel. Alonzo is 44 years old.
More Information
The problem involves translating word problems into algebraic expressions. The equation $x - 11 = 44$ models the relationship between Rachel's age ($x$) and Alonzo's age (44), where Alonzo is 11 years younger than Rachel.
Tips
A common mistake is misinterpreting the relationship between the ages and setting up the equation incorrectly. For instance, confusing "11 years younger" with addition instead of subtraction.
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