Person A buys 10 granola bars and 6 cups of yogurt for $18. Person B buys 5 granola bars and 4 cups of yogurt for $9.50. Find the cost of each item.

Answer 1

Let g be granola bars and y be yogurt.

Write two equations for person A and B for the total cost of their grocery trip with the number of corresponding items for granola bars and yogurt:

Person A: 10*g+6*y=18

Person B: 5*g+4*y=9.5

Two equations and two unknowns, so this is solvable. Multiply equation B by -2:

Person B: -10*g-8*y=-19

Add equation A and equation B to cancel out the g variable:

Person A: 10*g+6*y=18

Person B: -10*g-8*y=-19

---> 0*g-2*y=-1

Thus -2*y=-1, or y=0.5 or 50 cents each. Plug y = 0.5 into either equation to solve for cost of g (I'll use equation A):

Person A: 10*g+6*(0.5) = 18

Solving for g we have:

10*g=15 or g = 1.5, so the cost of the granola bar is $1.50.