# Irene has a total of 1686 red, blue and green balloons for sale. the ratio of the number of balloons to the number of blue balloon was 2: 3 .after irene sold 3/4 of the balloons, 1/2 of the green balloons and none of the red balloons, she has 922 balloons left. how many blue balloons did irene have at first?

Answers: 3

## Answers

Irene has a total of 1686 red, blue and green balloons for sale. the ratio of the number of balloons...

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.

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