irene had a total of 1686 red,blue and green balloons for sale.the ratio of red to blue was 2:3.after irene sold 3/4 blue and 1/2 red.she had 922 balloons left.hiw many blue balloons does irene have at first?

Guest Jul 6, 2015

#1**+10 **

Perhaps I've gone wrong somewhere or misinterpreted part of the question!

Edit: Of course, I made a numerical mistake towards the end. I should have had 13b/12 = 764 (giving b = 705.231), not 13b/4 = 764. Never-the-less, this still doesn't result in integer numbers of balloons!

.

Alan
Jul 6, 2015

#1**+10 **

Best Answer

Perhaps I've gone wrong somewhere or misinterpreted part of the question!

Edit: Of course, I made a numerical mistake towards the end. I should have had 13b/12 = 764 (giving b = 705.231), not 13b/4 = 764. Never-the-less, this still doesn't result in integer numbers of balloons!

.

Alan
Jul 6, 2015

#2**+5 **

irene had a total of 1686 red,blue and green balloons for sale.the ratio of red to blue was 2:3.after irene sold 3/4 blue and 1/2 red.she had 922 balloons left.hiw many blue balloons does irene have at first ?

$$\small{\text{$

\begin{array}{lrcl}

(1) & r + b + g &=& 1686 \\\\

(2) & \dfrac{r}{b} &=& \dfrac23 \qquad \text{ so } \qquad r = \dfrac23 \cdot b\\\\

\hline

\\

(2) \text{ in } (1): \quad & \dfrac23 \cdot b + b+ g &=& 1686 \\\\

(I) & \dfrac53 \cdot b + g &=& 1686 \\\\

\hline

\\

(3) & \dfrac14 \cdot b + \dfrac12 \cdot r +g &=& 922\\\\

(2) \text{ in } (3): \quad & \dfrac14 \cdot b +\dfrac12 \cdot \dfrac23 \cdot b + g &=& 922 \\\\

& \dfrac14 \cdot b +\dfrac13 \cdot b + g &=& 922 \\\\

& \dfrac3{12} \cdot b +\dfrac4{12} \cdot b + g &=& 922 \\\\

(II) & \dfrac7{12} \cdot b + g &=& 922 \\\\

\hline

\\

(I)-(II): & \dfrac53 \cdot b - \dfrac7{12} \cdot b &=& 1686 - 922 \\\\

& \dfrac53 \cdot b - \dfrac7{12} \cdot b &=& 764 \\\\

& \dfrac{20}{12} \cdot b - \dfrac7{12} \cdot b &=& 764 \\\\

& \dfrac{13}{12} \cdot b &=& 764 \\\\

& b &=& \dfrac{ 764\cdot 12 } {13} \\\\

&\mathbf{ b }& \mathbf{=}& \mathbf{705}

\end{array}

$}}$$

**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

heureka
Jul 6, 2015

#3**+5 **

No, Alan...I worked it out, too....there's no "whole" number answer possible based on the available info........

Let x = initial number red ....the (3/2)x = initial number blue .... y= initial number green

Before the sale, we have:

x + (3/2)x + y = 1686 → (5/2)x + y = 1686 (1)

After the sale, we have:

(1/2)x + (1/4)(3/2)x + y = 922 → (7/8)x + y = 922 (2)

Subtract (2) from (1)

(13/8)x = 764 x = about 470 initial red

(3/2)x = about 705 initial blue

Rats!!!.....heureka beat me to it !!!!!

CPhill
Jul 6, 2015