Introduction- order of operations word problems

The standard order of operations, or precedence, is expressed in the following chart.

Exponents and roots

Multiplication and division

Addition and subtraction

This means that if a number or other symbol, or an expression grouped by one or more symbols of grouping, is preceded by one operator and followed by another, the operator higher on the list
should be applied first in order of operations.

Source: Wikipedia

Concept- Order of Operations Word Problems

In long math problems with +,-,x,%,(), and exponents in them, you have to know what to do first. Without follow the identical rules, you may get different answers. You can easily keep in mind the
silly sentence, Please Excuse My Dear Aunt Sally, you can commit to memory the order of operations, and you must follow.

Please “P” stands for parentheses. You need to do operation in side parentheses first.

Excuse “E” stands for exponents, you must reduce exponents next.

My Dear “M” stands for multiply

“D” stands for division. Start on the left of the equation and perform all multiplication and divisions in the order in which they appear.

Aunt Sally “A” stands for addition.

“S”stands for subtract. Always on the left hand side and perform all additions and subtractions.

Examples for Order of Operations Word Problems:

Example 1:

Five years ago, Sam’s age was half of the age he will be in 10 years. How old is he now?

Solution:

Step 1: Let x be Sam’s age now. Look at the problem and put the significant expressions above it.

Five years ago x-5,

Sam’s age was half of the age(`1/2`) he will be in 10 years.

Step 2: copy out the equation in above word problem.

Note: we need to apply order of operations.

x-5=`1/2`(x+10)

x-5=`1/2`x+5

Isolate variable x

x-`1/2`x=5+5

`1/2`x=10

x=20

Answer: Sam is now 20 years old.

Example 2:

Alex’s father is 5 times older than Alex and Alex is twice as old as his brother nick. In three years time, the sum of their ages will be 58. How old is Alex now?

Solution:

Alex’s father is 5 times older than Alex and Alex is twice as old as his brother nick. In two years time, the addition of their ages will be 58. How old is Alex now?

Let a be Alex’s age now. Add 2 to get the ages in 3 yrs.

Alex’s (present age) is 5a, after 2 years is 5a+3.

Alex (present age) is a, after 2 years is a+3.

Nick (present age) is `1/2`a, after 2 years is `1/2`a+3

Write the new relationship in an equation using the ages in 3 yrs.

In three years time, the sum of their ages will be 58.

Note: we need to apply order of operations.

5a+3+a+3+`1/2`a+3=58

5a+a+`1/2`a=58-3-3-3

6`1/2`a=49

6x=98

x=`98/6`

x=`49/3`

x= 16 years 4months 10 days

Answer: Alex is now 16 years 4months 10days old.