SOLUTION: Anna bought 12 pieces of gum consisting of only red gumballs and white gumballs. The total cost is $1.29. The red gumballs each cost 3 cents more than each white gumball, and she b

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Question 259667: Anna bought 12 pieces of gum consisting of only red gumballs and white gumballs. The total cost is $1.29. The red gumballs each cost 3 cents more than each white gumball, and she bought fewer reds than whites. How many white gumballs did she buy? How many red?
Answer by Edwin McCravy(20060) About Me  (Show Source):
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Anna bought 12 pieces of gum consisting of only red gumballs and white gumballs. The total cost is $1.29. The red gumballs each cost 3 cents more than each white gumball, and she bought fewer reds than whites. How many white gumballs did she buy? How many red?


Ler R = thr number of red ones.

Let W = the number of white ones.

Let x = the price of each white ones.

Then x+3 = the price of each red one

So we have the system:

system%28R+%2B+W+=+12%2CR%28x%2B3%29+%2B+Wx+=+129%2C++R+%3C+W%29 

R(x+3) + Wx = 129

Rx + 3R + Wx = 129

Rx + Wx = 129-3R

x(R + W) = 129-3R

and since R + W = 12,

x(12) = 129-3R

12x + 3R = 129

4x + R = 43

R = 43-4x

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R + W = 12, so

W = 12 - R

W = 12 - (43-4x)

W = 12-43+4x

W = 4x-31

----------------

    R < W, so   

43-4x < 4x-31
  -8x < -74 
    x > 9.25

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Since R > 0,

43-4x > 0
  -4x > -43
    x < 10.75

So 9.25 < x < 10.75

The only whole number of cents possible between those
two values is 10 cents.

R = 43-4x = 43-4(10) = 43-40 = 3

W = 12 - R = 12 - 3 = 9

So there is one solution:

3 Reds, 9 Whites, Reds cost 10 cents each, Whites cost 13 cents each

Edwin