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

Write 2 equations with 2 unknowns. Let g = granola bar price and y = yogurt price

equation 1: 12g + 7y = 15.50

equation 2: 6g + 11y = 11.50

Use elimination.

Make equation 3: Multiply equation 2 by -2 to eliminate "g": -12g -22y = -23

Add equation 2 + equation 3:

12g -12g + 7y - 22y = 15.50 - 23

Add/subtract like terms: -15y = -7.50

Divide by -15: y = -7.50/-15 = .50 ⇒ y = $.50

Put "y" into either of the original equations to find "g":

12g + 7(.50) = 15.50

12g + 3.50 = 15.50

12g = 12

g = $1

CHECK:

6(1) + 11(.5) = 11.50

ANSWER: granola bars = $1, yogurt cups = $.50