Practicing Success
a b c d |
c |
$(x-8)(y+10)=xy$ $⇒xy-8y+10x-80=xy$ $5x-4y=40$ ...(1) or $10x-8y=80$ ...(2) $(x+16)(y-10)=xy$ $xy+16y-10x-160=xy$ $8y-5x=80$ ...(3) eq. (3) + eq. (2) We get, $5x=160$ $x=32$ → no. of children putting x in (1) we get, $y = 30$ → money spent on each child so money spent = $xy = 960$ Eq. (1) → $5x-4y=40$ Eq. (3) → $8y-5x=80⇒5x-8y=-80$ so matrix form is $\begin{bmatrix}5&-4\\5&-8\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}40\\-80\end{bmatrix}$ |