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?
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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(R + W = 12,R(x+3) + Wx = 129,  R < W)}}} 

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

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    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</pre>