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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?

 Sep 21, 2021

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 #1
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Let the number of roses at AF==A
Let the number of roses at BF==B


2/7A==3/4B
[A - 84] / [B + 58] ==3/2, solve for A, B

Use substitution to get:


A==399 roses - what Angel Florist started with
B==152 roses - what Beauty Florist started with.

 Sep 22, 2021
 #2
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A = 2/7 = 6/21

 

B = 3/4 = 6/8

 

A      =      B

21    :       8

- 84        +58

-------------------------

 3      :       2

 

21x - 84 = 3 parts

42x - 168 = 6 parts

8x + 58 = 2 parts

24x + 174 + 2 parts

42x - 168 = 24x + 174

 18x + 32

    x = 19

Total = 29 * 19 = 551

 Sep 23, 2021

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