At a college bookstore, Carla purchased a math textbook and a novel thjat cost a total of $54, not including tax. If the price if the math textbook, m, is $8 more than 3 times the price of the novel, n, write a system of linear equations that could be used to determine the price of each book?
m + n = 54
3n+8=m
plug in 3n+8 for m in the first equation
3n+8+n=54
4n+8=54
4n=46
n= $11.50 which means m= $42.50
Let's define our variables:
m = price of the math textbook
n = price of the novel
According to the given information:
1) The total cost of the math textbook and the novel is $54, not including tax:
m + n = 54 (Equation 1)
2) The price of the math textbook, m, is $8 more than 3 times the price of the novel, n:
m = 3n + 8 (Equation 2)
So, the system of linear equations that could be used to determine the price of each book is:
m + n = 54
m = 3n + 8
To write a system of linear equations, we need to assign variables to the unknown values and express the given information in equations. Let's assign "m" as the price of the math textbook and "n" as the price of the novel.
We are given that the total cost of both books is $54, so the first equation is:
m + n = 54
We are also given that the price of the math textbook, "m", is $8 more than 3 times the price of the novel, "n". Mathematically, this can be expressed as:
m = 3n + 8
Therefore, the system of linear equations is:
m + n = 54
m = 3n + 8
Solving this system of equations would give us the values of "m" and "n," which represent the price of the math textbook and the novel, respectively.
n=$11.50
m=$42.50