Question

“Total price of 7 pencils and 5 pens is 29” .Write down its algebraic form. \[\]

Answer 1

Hint: We recall the definitions constant, variable, the degree of the variable and algebraic form where degree on all the terms is equal. We denote the unknowns the price of one pencil as $x$ and the price of one pen as $y$ and then express the given statement in algebraic. \[\]

Complete step by step answer:
We know that an algebraic expression consists of variables whose values we do not know and constants whose value we know. The variables are commonly represented as by English small letters $x,y,z$ and the constants are numbers. For example in ${{x}^{2}}+7xy+5$ the variables are $x,y$ and the constants are 7 and 5. \[\]
The power on the variable is called the degree of the term. Here the degree on the term ${{x}^{2}}$ is 2, the degree on $7xy=7{{x}^{1}}{{y}^{1}}$ is $1+1=2$ and degree on $5=5{{x}^{0}}$ is 0. \[\]
We call algebraic equations or expressions to be in algebraic form when the degree of all the terms with variables will have the same degree. Since ${{x}^{2}}+7xy+5$ has variable terms ${{x}^{2}},7xy$ have degree 2 then it is in algebraic form .
We are asked in the question to express “Total price of 7 pencils and 5 pens is 29” in algebraic form. We try to find what we do not know when calculating the total price of 7 pencils and 5 pens. We do not know the price of one pencil or one pen. \[\]
Let assume the unknown price of one pencil by a variable $x$, then the price of 7 pencils will be 7 times $x$ that is
\[7\times x=7x\]
Let assume the unknown price of one pen by a variable $y$, then the price of 5 pens will be 5 times $y$ that is
\[5\times y=5y\]
The total price will be the sum of prices of 7 pencils and 5 pens that is $7x+5y$ but we are given that the total price is 29 so we have
\[7x+5y=29\]
The above equation is in algebraic form with degree 1 on each variable term.\[\]

Note: We note that the obtained algebraic form is an equation also called linear (because of degree 1) equation in two variables. The values of $x$ and $y$ for which the equation is satisfied are solutions of the equation. The other name of the algebraic form is homogeneous polynomial.