Question

The cost of a new CD is \[\$ 14.95\] , and the cost of a video game is \[\$ 39.99\]. How much would ‘c’ CDs and ‘v’ video games cost?

Answer 1

Hint: We know that mathematical expression and algebraic expression are both the same. An algebraic expression in mathematics is an expression which is made up of variables and constants along with algebraic operations. An expression is a group of terms. Here algebraic operations are addition, subtraction, division and multiplication etc.

Complete step by step solution:
We have,
The cost of a new CD is \[\$ 14.95\] , then ‘c’ number of CDs cost is \[ \Rightarrow c \times \$ 14.95\]
Similarly
Cost of a video game is \[\$ 39.99\] , then the ‘v’ number of video games cost is \[ \Rightarrow v \times \$ 39.99\] .
Now we have the cost of c’ number of CDs and ‘v’ number of video games. If we add these two will get the cost of c’ number of CDs and ‘v’ number of video games.
 \[ \Rightarrow c \times \$ 14.95 + v \times \$ 39.99\] . Where ‘c’ and ‘v’ are unknowns and if we know the number of CDs and video games we can find the price.
Let’s take an example,
For the same problem if they ask us to find the cost of 2 CDs and 1 video game.
Then all we need to do is substitute \[c = 2,v = 1\] .
 \[ \Rightarrow 2 \times \$ 14.95 + 1 \times \$ 39.99\]
 \[ \Rightarrow \$ 29.9 + \$ 39.99\]
 \[ \Rightarrow \$ 69.89\]
So, the correct answer is “ \[ \ c \times \$ 14.95 + v \times \$ 39.99\] ”.

Note: Algebra helps in converting a mathematical statement into an equation. We know if we have ‘more’ or ‘sum’ in the given sentence we use addition operation \[( + )\] . Similarly If we have ‘less’ or ‘difference’ we use subtraction \[( - )\] . If we have ‘quotient’ we use division operation \[( \div )\] . To define more generalized terms; we use algebra. It is a very vast branch of mathematics and is used in all the branches of mathematics like polynomial, linear equations, graphs, etc. and in daily life too.