Hi Amanda,
Let X = the cost of apples
Let Y = the cost of pears
Beth bought 6 apples and 4 pears for $14--> 6X + 4Y = 14
Bet bought 8 apples and 3 pears for 14.50-->8X + 3Y = 14.50
Let's multiply the top equation by 3 and the bottom fraction by 4 so that we'll end up with 12Y in each equation and then we'll subtract:
18X + 12Y = 42
-(32X + 12Y = 58)
------------------------
-14X = -16
Divide both sides by -14--> X = 1.14
Plug this into the first equation to solve for Y--> 6(1.14) + 4Y = 14
6.84 + 4Y = 14
4Y = 7.16
Y = 1.79
So apples cost $1.14 each and pears cost $1.79 each. You can plug into the second equation to confirm . . you should get close to $14.50. . . not exact because we rounded off to get 1.14
Dan
