Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our 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
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
