Person A buys10 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

10g + 6y = 18

5g + 4y = 9.5

multiplies the second equation by -2 and then adds to the first...

the g cancels, out

10g + 6y = 18

-10g + -8y = -19

-2y = -1

y = 1/2

yogurt costs 0.50 per cup and 10g + 6(0.5) = 18

10g + 3 = 18

10g = 15

g = 15/10 = 3/2 = $1.50

the granola bar costs $1.50

the yogurt costs 50 cents = $0.50

Answer 2

Let x = the cost of a granola bar

Let y = the cost of a cup of yogurt

10x + 6y = 18 Divide both sides of this equation by 2.

5x + 3y = 9

The second equation is 5x + 4y = 9.50. Now subtract the two equations.

5x + 4y = 9.50

-5x - 3y = -9

y = $.50

5x + 3(.50) = 9

5x + 1.50 = 9

5x = 7.5

x = $1.50