Irene had a total of 1686 red, blue and
green balloons for sale.
The ratio of the number of red balloons to
the number of blue balloons was 2:3.
After Irene sold 3/4 of the blue balloons, 1/2
of the green balloons and none of the red
balloons, she had 922 balloons left.
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How many blue balloons did Irene have at
first?
Sul
Answers
Answer :- 158 balloons
Solution:
Given that, Irene had a total of 1686 red, blue and green balloons for sale.
Let the number of red, blue and green balloons be x, y and z respectively.
∴ x + y + z = 1686 ...(1)
Also, Ratio of the number of red balloons to the number of blue balloons was 2 : 3
∴ 2x = 3y
⇒ x = 3y / 2 ...(2)
Substitute [x = 3y / 2] in (1) ,
⇒ (3y / 2 ) + y + z = 1686
⇒ ( 5y / 2 ) + z = 1686
⇒ 5y + 2z = 3372 ...(3)
Again, Irene sold 3/4 of the blue balloons & 1/2 of the green balloons and none of the red balloons She had 922 balloons left
∴ 3y / 4 + z/2 = 1686 - 922
⇒ (3y / 4) + z / 2 = 764
⇒ (3y + 2z) / 4 = 764
⇒ 3y + 2z = 3056 ...(4)
Subtract (3) from (4), we get
⇒ 3y + 2z - 5y - 2z = 3056 - 3372
⇒ -2y = -316
⇒ y = 158
Hence, Irene had 158 blue balloons at first.
Answer:
Step-by-step explanation:
Irene does have at first 705 blue balloons.
check: 176 ( blue ) + 235 ( red ) + 511 ( green ) = 922
705 ( blue ) + 470 ( red ) + 511 ( green ) = 1686
176 / 705 = 1 / 4
235 / 470 = 1 / 2
705 * ( 2 / 3 ) = 470