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?

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

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}

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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**