waecmaths question:
The sum of 2 consecutive whole numbers is $\tfrac{5}{6}$ of their product. Find the numbers
Option A:
3,4
Option B:
1,2
Option C:
2, 3
Option D:
0,1
waecmaths solution:
$\begin{align} & \text{Let the number be }(x-1)\text{ and }x \\ & \tfrac{5}{6}(x-1)x=x+(x-1) \\ & \tfrac{5}{6}({{x}^{2}}-x)=2x-1 \\ & 5{{x}^{2}}-5x=12x-6 \\ & 5{{x}^{2}}-17x+6=0 \\ & 5{{x}^{2}}-15x-2x-6=0 \\ & 5x(x-3)-2(x-3)=0 \\ & (5x-2)(x-3)=0 \\ & x=3\text{ or }x=\tfrac{2}{5} \\\end{align}$
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