SOLUTION: Marcia has 65 game pieces with a total value of 89 points. Each game piece is worth one or two points. How many two-point game pieces does she have?

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Question 246051: Marcia has 65 game pieces with a total value of 89 points. Each game piece is worth one or two points. How many two-point game pieces does she have?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = number of game pieces with 1 point.
y = number of game pieces with 2 points.

x + y = 65
1x + 2y = 89

use first equation so solve for y to get y = 65-x

substitute for y in second equation to get 1x + 2*(65-x) = 89

simplify to get 1x + 130 - 2x = 89

subtract 130 from both sides of equation to get 1x - 2x = 89 - 130

combine like terms to get -x = -41

multiply both sides of equation by -1 to get x = 41

if x = 41, then y = 24 because x + y = 65, and 41 + 24 = 65

as for the points:

41 * 1 = 41
24 * 2 = 48

41 + 48 = 89 so the point totals match up.

your answer is:

she has 24 game pieces worth 2 points each.