# SOLUTION: Two records and three tapes cost \$31. Three records and two tapes cost \$29. Find the cost of each record and each tape Let's call x the cost of records and y the cost of tapes.

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 Question 55038: Two records and three tapes cost \$31. Three records and two tapes cost \$29. Find the cost of each record and each tape Let's call x the cost of records and y the cost of tapes. As a side note, who really cares? Don't we all buy CDs if not MP3s now? Anyway, the first sentance in math-speak says: 2x + 3y = 31 And the second says 3x + 2y = 29 There are a few basic ways to tackle this problem: a) Addition method b) Substitution method c) Matrix method. d) Graph method I think I'm a fan of the substitution. we'll take the first equation and solve for x 2x + 3y = 31 Subtracting 3y from both sides gives 2x = -3y + 31 And divide by two. x = -3/2y + 31/2 Ok...now we take the second equation 3x + 2y = 29 and substitute x = -3/2y +31/2 in for x 3(-3/2y +31/2) +2y = 29 Now, we'll simplify the whole mess. -9/2y + 93/2 + 2y = 29 Combine like terms -5/2y + 93/2 = 29 Moving the 93/2 to the right side yields -5/2y = 58/2 - 93/2 -5/2y = -35/2 dividing by -5/2 gives y = -35/2(-2/5) y = 7 Ok...y = 7! Let's sub that into one of our original equations and solve for x. 2x + 3(7)=31 2x + 21 = 31 2x = 10 x=5 We've got x=5 and y = 7. Lets check our answers with the second equation just to make sure we've got it. 3(5) + 2(7) = 29 15+14=29 29=29 Yep..we did it right! Records are \$5 and Tapes are \$7Answer by Hook(36)   (Show Source): You can put this solution on YOUR website!Let's call x the cost of records and y the cost of tapes. As a side note, who really cares? Don't we all buy CDs if not MP3s now? Anyway, the first sentance in math-speak says: 2x + 3y = 31 And the second says 3x + 2y = 29 There are a few basic ways to tackle this problem: a) Addition method b) Substitution method c) Matrix method. d) Graph method I think I'm a fan of the substitution. we'll take the first equation and solve for x 2x + 3y = 31 Subtracting 3y from both sides gives 2x = -3y + 31 And divide by two. x = -3/2y + 31/2 Ok...now we take the second equation 3x + 2y = 29 and substitute x = -3/2y +31/2 in for x 3(-3/2y +31/2) +2y = 29 Now, we'll simplify the whole mess. -9/2y + 93/2 + 2y = 29 Combine like terms -5/2y + 93/2 = 29 Moving the 93/2 to the right side yields -5/2y = 58/2 - 93/2 -5/2y = -35/2 dividing by -5/2 gives y = -35/2(-2/5) y = 7 Ok...y = 7! Let's sub that into one of our original equations and solve for x. 2x + 3(7)=31 2x + 21 = 31 2x = 10 x=5 We've got x=5 and y = 7. Lets check our answers with the second equation just to make sure we've got it. 3(5) + 2(7) = 29 15+14=29 29=29 Yep..we did it right! Records are \$5 and Tapes are \$7