# Linear Equations in worded problems

__Date: May 19, 2020__

__Date: May 19, 2020__

__Subject: Mathematics__

__Subject: Mathematics__

__Topic: Algebra – Worded problems__

__Topic: Algebra – Worded problems__

### Worded problems in algebra requires you to write an expression or equation by converting the words in the problem to a problem in math language.

### The following terms will assist you in converting from words to numbers and symbols.

### Increased by——means to add

### Decreased by—–means to subtract

### Less than —– subtract but pay attention to the order of the numbers

### Times —— means to multiply

### More than ——- means to add

### Sum —— means to add

### Difference —— means to subtract

### A number ——– Any letter or symbol

### Is ——– Equals

### Product ——- means to multiply

### Example: A number increased by 5 is 15. What is the number?

### Let us call the number Y. Therefore we can write

### Y + 5 = 15

### Then we solve by subtracting 5 from both sides

### Y + 5 – 5 = 15 – 5

### Y = 10

### Example: Six less than a number is 4, what is the number?

### In this example if you wrote 6- X = 4 you would be wrong

### We would write it as X – 6 = 4…..since 6 is less than we are subtracting 6.

### X – 6 = 4

### We solve now by adding 6 to both sides

### X – 6 + 6 = 4 + 6

### X = 10

### Example: 5 times a number is 25, what is the number.

### We can call the number B and would write the equation as:

### 5 x B = 25 or 5B = 25

### To solve we divide by 5:

### 5B/5 = 25/ 5; therefore B = 5