mini has some pencils.if she gives 3 pencils to each pupil,she will have 20 pencils left.if she gives 4pencils to each pupil, she will have none left.how many pencils does she have

Dear student,

Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{total} \mathrm{number} \mathrm{of} \mathrm{people} \mathrm{be} \text{'}\mathrm{x}\text{'} \\ \mathrm{It} \mathrm{is} \mathrm{given} \mathrm{that} \mathrm{if} \mathrm{she} \mathrm{gives} 3 \mathrm{pencils} \mathrm{to} \mathrm{each} \mathrm{pupil}, \mathrm{she} \mathrm{is} \mathrm{left} \mathrm{with} 20 \mathrm{pencils} \\ \mathrm{So} \mathrm{the} \mathrm{total} \mathrm{number} \mathrm{of} \mathrm{pencils} \mathrm{are} \mathbf{3}\mathbf{x}\mathbf{+}\mathbf{20} \\ \mathrm{Also} \mathrm{it} \mathrm{is} \mathrm{given} \mathrm{that} \mathrm{if} \mathrm{she} \mathrm{gives} 4 \mathrm{pencils} \mathrm{to} \mathrm{each} \mathrm{pupil}, \mathrm{she} \mathrm{will} \mathrm{have} \mathrm{n} \\ \mathrm{left}. \mathrm{So} \mathrm{the} \mathrm{total} \mathrm{number} \mathrm{of} \mathrm{pencils} \mathrm{can} \mathrm{also} \mathrm{be} \mathrm{expressed} \mathrm{as}\mathbf{ }\mathbf{4}\mathbf{x} \\ \mathrm{This} \mathrm{implies} \mathrm{that}, \\ 4\mathrm{x}=3\mathrm{x}+20 \\ 4\mathrm{x}-3\mathrm{x}=20 \\ \mathrm{x}=20 \\ \mathrm{This} \mathrm{implies} \mathrm{that} \mathrm{the} \mathrm{total} \mathrm{number} \mathrm{of} \mathrm{pencils} \mathrm{are}, \\ 3\left(20\right)+20=60+20\mathbf{=}\mathbf{80} \end{gathered}$$

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