Short answer linear equation

Question

A shopkeeper mixed a herb worth $2.50 a kg with another herb worth $3.50 a kg. He sold 20kgs of the mixture at $2.8 per kg. Find the weights of the two different herbs e mixed together. 

Answer 1

Hi Rav,

 

Let's set this up.

 

x = # kg of $2.50 herb 

y = # kg of $3.50 herb

 

From the 2nd sentence, we have the following equations.

x + y = 20

2.5x + 3.5y = 20(2.8)

 

The elimination method requires you to eliminate one variable when adding the two equations together.  In order to do this, we can multiply the first equation by -2.5 (or -3.5).

 

-2.5x - 2.5y = 20(-2.5)  

2.5x + 3.5y = 20(2.8)

 

-2.5x - 2.5y = -50 
2.5x + 3.5y = 56

 

Adding them together

 

y = 6

 

And since x+y=20, x = 14