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### From Sentences to Equations

- To write an equation based on a given sentence, use a variable to represent the unknown quantity. Write verbal expressions as algebraic expressions.
- Recognize that the following verbal expressions mean = : is, is the same as, is identical to.
- Solve word problems using these steps: investigate the problem, plan a solution, solve the problem, and check the solution.
- Be able to translate verbal statements into mathematical formulas.

### From Sentences to Equations

Write the equation for:

Six times a number decreased by the square of that number is three more than five times the number.

Six times a number decreased by the square of that number is three more than five times the number.

- x represents the unknown number

**6**

**x**−

**x**

^{2}

**=**

**5**

**x**

**+**

**3**

Write the equation for:

Eight times the sum of a number and the cube of another number is ten less than the difference of the second number and four times the first number.

Eight times the sum of a number and the cube of another number is ten less than the difference of the second number and four times the first number.

- x = 1st number

y = 2nd number

**8**

**(**

**x**

**+**

**y**

^{3}

**)**

**=**

**(**

**y**−

**4**

**x**

**)**−

**10**

Write the equation for: Twelve times a number increased by the cube of that number is twenty more than eight times the number.

- x represents the unknown number

**12**

**x**

**+**

**x**

^{3}

**=**

**8**

**x**

**+**

**20**

Write the equation for:

Sixteen times the difference of a number and half of another number is three less than the sum of the square of the second number and seven times the first number.

Sixteen times the difference of a number and half of another number is three less than the sum of the square of the second number and seven times the first number.

- x = 1st number

y = 2nd number

**16**

**(**

**x**− [(

**y**)/(

**2**)]

**)**

**=**

**(**

**y**

^{2}

**+**

**7**

**x**

**)**−

**3**

Write the equation for:

John's brother is ten years younger than he is. The product of their ages is seventeen less than the square of the difference of their ages.

John's brother is ten years younger than he is. The product of their ages is seventeen less than the square of the difference of their ages.

- j = John's age

j - 10 = John's sister's age - j(j − 10) = [j − (j − 10)]
^{2}− 17 - j(j − 10) = (j − j + 10)
^{2}− 17 - j(j − 10) = 10
^{2}− 17 - j(j − 10) = 100 − 17

**j**

**(**

**j**−

**10**

**)**

**=**

**83**

Write the equation for:

Jason's friend is six years older than he is. The difference of their age is three times Jason's age.

Jason's friend is six years older than he is. The difference of their age is three times Jason's age.

- j = Jason's age

j + 6 = Jason's friend's age

**j**−

**(**

**j**

**+**

**6**

**)**

**=**

**3**

**(**

**j**

**+**

**6**

**)**

Write the equation for: The square of a number decreased by ten times that number is two less than five times that number.

- x represents the unknown number

**x**

^{2}−

**10**

**x**

**=**

**5**

**x**−

**2**

Write the equation for:

Half of a number is seven more than four times the square of that number.

Half of a number is seven more than four times the square of that number.

- x represents the unknown number

[(

**x**)/(**2**)]**=****4****x**^{2}**+****7**Write the equation for:

Nine times the difference of a number and the cube of another number is seven more than the difference of two times the square of the second number and three times the first number.

Nine times the difference of a number and the cube of another number is seven more than the difference of two times the square of the second number and three times the first number.

- x = 1st number

y = 2nd number

**9**

**(**

**x**−

**y**

^{3}

**)**

**=**

**(**

**2**

**y**

^{2}−

**3**

**x**

**)**

**+**

**7**

Write the equation for:

Sarah's sister is twice her age. The sum of their ages is three less than the square of the difference of their ages.

Sarah's sister is twice her age. The sum of their ages is three less than the square of the difference of their ages.

- s = Sarah's age

2s = Sarah's sister's age

**s**

**+**

**2**

**s**

**=**

**(**

**s**−

**2**

**s**

**)**

^{2}−

**3**

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### From Sentences to Equations

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Real World Applications
- Strategy 0:26
- Using Variables
- Translate Phrases
- Identity Equality Words
- Example 1: Write Equation 1:32
- Example 2: Write Equation 4:14
- Example 3: Sisters' Ages 8:26
- Example 4: Surface Area of Cylinder 12:52

1 answer

Last reply by: Dr Carleen Eaton

Tue Apr 26, 2016 7:45 PM

Post by Raymond Hayden on April 24 at 11:45:01 PM

Regarding Ex #3, the right side of the equation = 20 because the difference between the two ages is 5 and 5sq = 25 and 25-5 = 20. The left side of the equation is a problem because the are no multiples of 20 that have a difference of 5 between them. This makes the equation untrue. Am I correct?

1 answer

Last reply by: Dr Carleen Eaton

Wed Jun 26, 2013 11:38 PM

Post by Taylor Wright on June 17, 2013

In example 3:

Wouldn't (m-(m-5)) be (m-m+5) which would be 5 ?

Shouldn't the minus sign in front of the parentheses distribute to the 5, turning it into a positive #?

2 answers

Last reply by: Raymond Hayden

Sun Apr 24, 2016 11:43 PM

Post by Taylor Wright on June 17, 2013

What are some good indicators that parentheses needs to be present?

1 answer

Last reply by: Dr Carleen Eaton

Thu Dec 27, 2012 12:15 AM

Post by bo young lee on December 17, 2012

i dont understand the example 1 and 2 can you explain more specific and more easy

1 answer

Last reply by: Dr Carleen Eaton

Tue May 11, 2010 11:56 PM

Post by eric filler on April 21, 2010

I enjoy this it is a whole diffrent way of looking at math thanks oh is their any work problems I can get for each lesson