Monday Balloon Calculation

Given ratios $P:Gr = 3:2$ and $P:G = 3:4$. The combined ratio $P:G:Gr$ is $3:4:2$. Sum of parts = $3+4+2 = 9$. The value of 1 part = $450 / 9 = 50$. Grey balloons ($Gr$) = $2 \times 50 = 100$.

$Gr_{\text{Mon}} = 100$

Tuesday Balloon Calculation

Let $Gr_T = 8x$, then $G_T = 9x$. Since $P_T = 1.375 \times Gr_T$, we get $P_T = 1.375 \times 8x = 11x$. Given $P_T - G_T = 40$, substitute the values: $11x - 9x = 40 \Rightarrow 2x = 40 \Rightarrow x = 20$.

$x = 20$

Total Tuesday Balloons

Find individual counts: $P_T = 11 \times 20 = 220$, $G_T = 9 \times 20 = 180$, $Gr_T = 8 \times 20 = 160$. Total Tuesday balloons = $220 + 180 + 160 = 560$.

$T_{\text{Tue}} = 560$

Final Difference

Calculate the difference between Tuesday total and Monday grey: $560 - 100 = 460$.

$560 - 100 = 460$