# algebra 1

ana bought 12 pieces of gum consisting of only red gum and white gums. The total cost was 1.29 the red gums each cost .03 more than each white gum and she bought fewer red gums than white gums. How many white gums did she buy?

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1. let the number of reds be r, let the number of whites be w

r + w = 12 and r<w and both r and w must be whole numbers

let the price of a white be x cents, then the price of a red is x+3 cents.
clearly x also must be a whole number.

then r(x+3) + wx = 129
rx + 3r + wx = 129
x(r+w) = 129-3r, but r = 12-w
x(12-w+w) = 129-3r

x = (129-3r)/12

we stated that x had to be a whole number, and the only choices for r are:
0,1,2,3,4,5

the only value which gives a whole number for x is when r = 3
then w = 9, and x = 10
so a white costs 10 cents, and a red costs 13 cents.

but 3(10) + 9(13) is not equal to 129

so your data is inconsistent and there is no solution to your question.

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2. Arhgghhh!!!!

Ignore the last two lines of my previous posts, I subbed in the price for the wrong colours.

Obviously 3(13) + 9(10) = 129

So there were 3 reds and 9 whites.

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3. idk, I don't understand the problem

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