Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
If Javier paid $92 for 5 notebooks and 3 pencils and Laura paid $56 for 2 notebooks and 6 pencils, then the price of each notebook is $16 and that of each pencil is $4, calculated using linear equations.
As per question statement, Javier paid $92 for 5 notebooks and 3 pencils while Laura paid $56 for 2 notebooks and 6 pencils.
We are required to calculate the price of each notebook and each pencil.
To solve this question, let us assume that the price of each notebook is "x" and that of each pencil is "y". Now, we will form two linear equations, each with the two assumed variables, based on the conditions mentioned in the question statement, and solving the equations, we will obtain our desired answer.
Since Javier bought 5 notebooks and 3 pencils for $92 and the price of each notebook is assumed to be "x" and that of each pencil is assumed to be "y", we can write that
[tex][(5x+3y)=92]...(1)\\or,5x = 92-3y\\or,x=\frac{(92-3y)}{5}...(2)[/tex]
And in Laura's case, she bought 2 notebooks and 6 pencils for $56, i.e.,
[tex][(2x+6y)=56]...(3)\\or, 2(x+3y)=56\\or, (x+3y)=\frac{56}{2}\\ or,(x+3y)=28\\or,x=(28-3y)...(4)[/tex]
Now, equating (2) and (4), we get,
[tex]x=\frac{(92-3y)}{5}=(28-3y)\\ or, \frac{(92-3y)}{5}=(28-3y)\\ or, (92-3y)=5(28-3y)\\or, 92-3y=140-15y\\or,(15y-3y)=140-92\\or,12y=48\\or,y=\frac{48}{12}=4[/tex]i.e., Price of each pencil is $4.
Now, using (y = 4) in the equation (4), we get,
[tex]x=[28-(3*4)]\\or,x=(28-12)\\or,x=16[/tex]i.e., Price of each notebook is $16.
Hence, the correct answer is
option(C) $16 for a notebook and $4 for a pencil.
- linear equations: In Mathematics, a linear equation is an algebraic equation which when graphed, always results in a straight Line and hence comes the name "Linear". Here, each term has an exponent of 1 and is often denoted as (y = mx + c) where, 'm' is the slope and 'b' is the y-intercept. Occasionally, it is also called as a "linear equation of two variables," where y and x are the variables.
- Variable: n Mathematics, a variable is a symbol or a representative of a value, which is unknown.
To learn more about Linear Equations, click on the link below.
brainly.com/question/27664510
#SPJ9
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
