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:
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