3x articles cost $( 7x+2) and 4(x+1) of the sam articles cost $( 12x+2 ). Fnd x

Question

Could you please use applications leading to quadratic equations thanks

Answer 1

(Number of items bought)*(Cost per item) = Cost

 

Let c = the Cost per item:

 

3x articles cost $( 7x+2):

3x*c = 7x+2

c = (7x+2)/3x

 

4(x+1) of the same articles cost $(12x+2) (=2(6x+1)):

4(x+1)*c = 2(6x+1)

c = 2(6x+1)/4(x+1) = (6x+1)/2(x+1)

 

Since the cost per item, c, is the same, set the two c equations equal:

 

(7x+2)/3x = (6x+1)/2(x+1)

 

(7x+2)*2(x+1) = (6x+1)*3x

 

14x² + 14x + 4x + 4 = 18x² + 3x

 

0 = 4x² - 15x - 4

 

0 = (4x+1)(x-4)

 

x = -1/4 and 4

 

Since you can't purchase -1/4 of an item, x = 4.