SOLUTION: The number 100 is separated into two parts such that if 1/3 of one part is subtracted from 1/4 of the other, the difference is 11. Find the two parts. Write your answers in asce

Question 1098063: The number 100 is separated into two parts such that if 1/3 of one part is subtracted from 1/4 of the other, the difference is 11. Find the two parts.
Write your answers in ascending order.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
100 = x + y

1/4 * x - 1/3 * y = 11

multiply both sides by 12 to get:

3 * x - 4 * y = 132

solve for x to get x = (4y + 132) / 3

replace x with it's equivalent value and your original equation of 100 = x + y becomes:

100 = (4y + 132) / 3 + y

multiply both sides of this equation by 3 to get:

300 = 4y + 132 + 3y

combine like terms to get 300 = 7y + 132

solve for y to get y = (300 - 132) / 7

this results in y = 24

since 100 = x + y, then x must be equal to 76 when y = 24.

1/4 * x - 1/3 * y = 11 becomes 1/4 * 76 - 1/3 * 24 = 11 which becomes 19 - 8 = 11 which becomes 11 = 11 which is true.

the two parts are 24 and 76 in ascending order.

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