EVALUATING REAL WORLD EXPRESSIONS

Evaluating real world expressions :

An algebraic expression is an expression that contains one or more variables and may also contain operation symbols, such as + or -

We can solve many real world problems by evaluating algebraic expressions. 

Example 1 : 

A scientist measures the air temperature in Death Valley, California, and records 50 °C. The expression

1.8c + 32

gives the temperature in degrees Fahrenheit for a given temperature in degrees Celsius c. Find the temperature in degrees Fahrenheit that is equivalent to 50 °C.

Solution : 

Step 1 :

Fromm the given information, we have 

c  =  50 °C

Step 2 :

Plug the value into the expression.

1.8c + 32

Plug 50 for c 

1.8(50) + 32

Multiply 

90 + 32

Add

122

Hence, 122 °F is equivalent to 50 °C.

Example 2 : 

The expression 6x² gives the surface area of a cube, where x is the length of one side of the cube. Find the surface area of a cube with a side length of 2 meters.

Solution : 

Step 1 :

Fromm the given information, we have 

x  =  2

Step 2 :

Plug the value into the expression which represents surface area of the cube.

6x²

Plug 2 for x 

6(2)²

Evaluate exponents

6(4)

Multiply 

24

Hence, the surface area of the cube 24 m²

Example 3 : 

The expression x³ gives the volume of a cube, where x is the length of one side of the cube. Find the volume of a cube with a side length of 2 meters.

Solution : 

Step 1 :

Fromm the given information, we have 

x  =  2

Step 2 :

Plug the value into the expression.

x³

Plug 2 for x 

(2)³

Evaluate exponents 

8

Hence, the volume of the cube 8 m3

Example 4 : 

The expression 60m gives the number of seconds in m minutes. How many seconds are there in 7 minutes?

Solution : 

Step 1 :

Fromm the given information, we have 

m  =  7

Step 2 :

Plug the value into the expression.

60m

Plug 7 for m 

60(7)

Multiply 

420

Hence, there are 420 seconds in 7 minutes. 

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