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Question Number 187817 by normans last updated on 22/Feb/23

Answered by mr W last updated on 22/Feb/23

Commented by mr W last updated on 22/Feb/23

$$c+d=9/3=3$$$$d+e=7/2$$$$c+e=(9+7)/5=16/5$$$$\Rightarrow 2d=3+7/2-16/5$$$$\Rightarrow d=33/20$$$$\Rightarrow c=3-33/20=27/20$$$$\Rightarrow e=7/2-33/20=37/20$$$$b+c=Y/4$$$$b+d=(Y+9)/7$$$$b+e=(Y+9+7)/9$$$$e+d-2c=(Y+9)/7+(Y+16)/9-2Y/4$$$$37/20+33/20-2\times 27/20=9/7+16/9-31Y/126$$$$\Rightarrow Y=46/5$$$$\Rightarrow b=46/5/4-27/20=19/20$$$$a+b=X/5$$$$a+c=(X+Y)/9$$$$b-c=X/5-X/9-Y/9$$$$19/20-27/20=4X/45-46/5/9$$$$\Rightarrow X=7✓$$

Commented by normans last updated on 22/Feb/23

$$nicesolution$$

Answered by mr W last updated on 23/Feb/23

Commented by mr W last updated on 23/Feb/23

$$B_2=\frac{3}{5}{X}_2$$$$C_2=\frac{2}{5}{X}_2$$$$\frac{A_1+X_1}{X_1}={\left(\frac{4+5}{5}\right)}^2=\frac{81}{25}$$$$\frac{B_1+A_1+X_1}{X_1}={\left(\frac{3+4+5}{5}\right)}^2=\frac{144}{25}$$$$\frac{C_1+B_1+A_1+X_1}{X_1}={\left(\frac{2+3+4+5}{5}\right)}^2=\frac{196}{25}$$$$\Rightarrow \frac{C_1}{X_1}=\frac{196-144}{25}=\frac{52}{25}$$$$\Rightarrow \frac{B_1}{X_1}=\frac{144-81}{25}=\frac{63}{25}$$$$B=B_1+B_2=\frac{63}{25}{X}_1+\frac{3}{5}{X}_2=9...\left(i\right)$$$$C=C_1+C_2=\frac{52}{25}{X}_1+\frac{2}{5}{X}_2=7...\left(ii\right)$$$$63X_1+15X_2=225$$$$52X_1+10X_2=175$$$$\Rightarrow X_1=\frac{225\times 10-175\times 15}{63\times 10-52\times 15}=2.5$$$$\Rightarrow X_2=\frac{225\times 52-175\times 63}{15\times 52-10\times 63}=4.5$$$$\Rightarrow X=X_1+X_2=2.5+4.5=7✓$$

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