Question

Person A buys 12 granola bars and 7 cups of yogurt for $15.50. Person B buys 6 granola bars and 11 cups of yogurt for $11.50. Find the cost of each item.

Answer 1

Let us assume that cost of each granola bar be $x and that of a cup of yogurt be $y  
From person A's purchase, we get  
12x + 7y = 15.5; equation A  
And from person B's purchase, 
6x + 11y = 11.5; equation B  
Let us multiply equation B by 2 and subtracting equation A from it, we will get  
12x + 22y - 12x - 7y = 23 - 15.5,  
=> 15y = 7.5 
or, y = 0.5  
Substituting value of y in equation A, we can find x  
12x + 7*0.5 = 15.5 
=> x = (15.5 - 3.5)/12 
or, x = 1  
Therefore, cost of granola bar is $1, and that of yogurt is $0.5