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At a college bookstore,Carla purchased a math textbook and a novel that cost a total of $54,not including tax. If the price of the math textbook ,m, is $8 more than 3 times the price of the novel,n, which system of linear equations could be used to determine the price of each book? ​

Respuesta :

Answer:

The price of novel is$ 11.5  

The price of math textbook $ 42.5

Step-by-step explanation:

Given as :

The total cost of the Math textbook and novel = $54

The price of the math textbook = $ m

The price of the novel = $ n

And, The price of the math textbook  is $8 more than 3 times the price of the novel .

According to question

The price of math textbook = 3 times the price of novel + $ 8

Or, $ m = 3 × $ n + $ 8

I.e m = 3 n + 8                  ...........A

And

The total cost of the Math textbook and novel = The price of the math textbook + The price of the novel

Or,  $ m + $ n = $ 54

I.e m + n = 54                      ..........B

Solving equation A and B

So, putting the value of m from A to eq B

Or , ( 3 n + 8 ) + n = 54

Or, 3 n + n + 8 = 54

Or, 4 n = 54 - 8

or, 4 n = 46

∴ n = [tex]\frac{46}{4}[/tex]

I.e n = [tex]\frac{23}{2}[/tex] = $ 11.5

So, The price of novel = n = $ 11.5

Again, put the value of n in Eq B

So, m = 54 - n

I.e m = 54 - 11.5

∴  m = $ 42.5

So, The price of math textbook = m = $ 42.5

Hence , The price of novel is$ 11.5  And The price of math textbook $ 42.5 Answer

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