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.

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 $7
Answer 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
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