Question

2/7 of the number of roses in Angel Florist was equal to 3/4 of the number of roses in Beauty Florist at first. After Angel Florist sold 84 roses and Beauty Florist bought another 58 roses, the ratio of the number of roses in Angel Florist to the number of roses in Beauty Florist became 3:2. What was the total number of roses in Angel Florist and Beauty Florist at first?
2/7 a = 3/4 b
(a-84)/(b+58) = 3/2
now solve as usual, then figure a+b
oobleck
original:
number in Angel's place --- a
number in Beauty's place --- b
(2/7)a = (3/4)b
8a = 21b or a = 21b/8

after transactions:
number for Angle = a - 84
number for Beauty = b + 58

(a-84)/(b+58) = 3/2
2a - 168 = 3b + 174
but from earlier: a = 21b/8
2(21b/8) - 168 = 3b + 174
21b/4 = 3b + 342
times 4
21b = 12b + 1368
9b = 1368
b = 152 , then a = 21(152)/8 = 399

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