SOLUTION: John had a total of 319 blue and red envelopes. If 1/3 the number of blue envelopes was the same as 2/5 the number of red envelopes, how many blue envelopes did he have?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: John had a total of 319 blue and red envelopes. If 1/3 the number of blue envelopes was the same as 2/5 the number of red envelopes, how many blue envelopes did he have?      Log On


   

Question 1195103: John had a total of 319 blue and red envelopes. If 1/3 the number of blue envelopes was the same as 2/5 the number of red envelopes, how many blue envelopes did he have?
Found 3 solutions by MathLover1, greenestamps, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
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let blue envelopes be b and red envelopes r

John had a total of 319: so,

b%2Br=319.........eq..1

If 1%2F3 the number of blue envelopes was the same as 2%2F5 the number of red envelopes, we have

%281%2F3%29b=%282%2F5%29r
b=%28%282%2F5%29%2F%281%2F3%29%29r
b=%286%2F5%29r

go to

b%2Br=319.........eq..1, substitute b
%286%2F5%29r%2Br=319.........solve for r
%2811%2F5%29r=319
r=319%2F%2811%2F5%29
r=319%2A%285%2F11%29
r=145

go to

b=%286%2F5%29r.....substitute r
b=%286%2F5%29145
b=174

John did have 174 blue envelopes.


Answer by greenestamps(13200) About Me  (Show Source):
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Rewrite the fractions with a common denominator: 1/3 = 5/15 of the number of blue envelopes is the same as 2/5 = 6/15 of the red envelopes.

That means the ratio of blue envelopes to red envelopes is 6:5.

So let the numbers of blue and red envelopes be 6x and 5x, respectively; then the total of 319 envelopes is 6x+5x=11x.

11x = 319
x = 319/11 = 29

ANSWER: The number of blue envelopes is 6x = 6*29 = 174

Answer by MathTherapy(10553) About Me  (Show Source):
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John had a total of 319 blue and red envelopes. If 1/3 the number of blue envelopes was the same as 2/5 the number of red envelopes, how many blue envelopes did he have?
Let number of blue envelopes be B
Then number of red envelopes = 319 - B
As 1%2F3 of the blue is the same as 2%2F5 of the red, we get: 

 5B = 6(319 - B) ----- Cross-multiplying
 5B = 1,914 - 6B
11B = 1,914
Number of blue, or