Two games and five puzzles cost $33.25 altogether. Three games and two puzzles cost $32.00. If every
game costs the same amount, and every puzzle costs the same amount, what is the cost of each puzzle?
x = cost of 1 game
y = cost of 1 puzzle 2x + 5y = 33.25 {two games and five puzzles cost $33.25} 3x + 2y = 32 {three games and two puzzles cost 32} 3(2x + 5y = 33.25) {multiplied top equation by 3} 2(3x + 2y = 32) {multiplied bottom equation by 2} 6x  15y = 99.75 {new top equation} 6x + 4y = 64 {new bottom equation}  11y = 35.75 {added the two new equations, eliminating the x} y = 3.25 {divided each side by 11} 3x + 2y = 32 {original bottom equation} 3x + 2(3.25) = 32 {substituted 3.25, in for y, into bottom original equation} 3x + 6.5 = 32 {multiplied 2 by 3.25} 3x = 25.5 {subtracted 6.5 from each side} x = 8.5 {divided each side by 3} cost of each game is $3.25 cost of each puzzle is $8.50 Ask the House
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