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?

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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)   (Show Source): You can put this solution on YOUR website!
let blue envelopes be and red envelopes

John had a total of : so,

.........eq..1

If the number of blue envelopes was the same as the number of red envelopes, we have





go to

.........eq..1, substitute
.........solve for





go to

.....substitute



John did have blue envelopes.


Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


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(10555)   (Show Source): You can put this solution on YOUR website!

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  of the blue is the same as  of the red, we get: 

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

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