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Question Number 101425 by pete last updated on 02/Jul/20

A student wrote three papers in mathematics examinations. Her marks for the two of papers were 77 and 72 respectively. To obtain grade A, an average of not less than 75 marks is required for the three papers. How many marks must she get in the third paper to get grade A?

$$\mathrm{A}\:\mathrm{student}\:\mathrm{wrote}\:\mathrm{three}\:\mathrm{papers}\:\mathrm{in}\:\mathrm{mathematics} \\ $$$$\mathrm{examinations}.\:\mathrm{Her}\:\mathrm{marks}\:\mathrm{for}\:\mathrm{the}\:\mathrm{two}\:\mathrm{of} \\ $$$$\mathrm{papers}\:\mathrm{were}\:\mathrm{77}\:\mathrm{and}\:\mathrm{72}\:\mathrm{respectively}.\:\mathrm{To} \\ $$$$\mathrm{obtain}\:\mathrm{grade}\:\mathrm{A},\:\mathrm{an}\:\mathrm{average}\:\mathrm{of}\:\mathrm{not}\:\mathrm{less} \\ $$$$\mathrm{than}\:\mathrm{75}\:\mathrm{marks}\:\mathrm{is}\:\mathrm{required}\:\mathrm{for}\:\mathrm{the}\:\mathrm{three} \\ $$$$\mathrm{papers}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{marks}\:\mathrm{must}\:\mathrm{she}\:\mathrm{get} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{third}\:\mathrm{paper}\:\mathrm{to}\:\mathrm{get}\:\mathrm{grade}\:\mathrm{A}? \\ $$

Commented by Rasheed.Sindhi last updated on 02/Jul/20

Arithmatic approach 77=75+2 72=75−3 +2−3=−1 To balance this −1 : 75+1=76 At least 76 in third paper

$$\mathcal{A}{rithmatic}\:{approach} \\ $$$$\mathrm{77}=\mathrm{75}+\mathrm{2} \\ $$$$\mathrm{72}=\mathrm{75}−\mathrm{3} \\ $$$$+\mathrm{2}−\mathrm{3}=−\mathrm{1} \\ $$$${To}\:{balance}\:{this}\:−\mathrm{1}\:: \\ $$$$\mathrm{75}+\mathrm{1}=\mathrm{76} \\ $$$${At}\:\:{least}\:\mathrm{76}\:{in}\:{third}\:{paper} \\ $$

Commented by pete last updated on 03/Jul/20

thanks sir

$$\mathrm{thanks}\:\mathrm{sir} \\ $$

Answered by Rasheed.Sindhi last updated on 02/Jul/20

((77+72+x)/3)=75 ; x: at least marks in 3rd paper x=75×3−77−72=76

$$\frac{\mathrm{77}+\mathrm{72}+{x}}{\mathrm{3}}=\mathrm{75}\:;\:{x}:\:{at}\:{least}\:{marks}\:{in}\:\mathrm{3}{rd}\:{paper} \\ $$$${x}=\mathrm{75}×\mathrm{3}−\mathrm{77}−\mathrm{72}=\mathrm{76} \\ $$$$ \\ $$

Answered by Rasheed.Sindhi last updated on 02/Jul/20

Let at least marks in 3rd paper: 75+x; x∈Z 77=75+2 72=75−3 ? =75+x +2−3+x=0⇒x=1 75+x=75+1=76

$${Let}\:{at}\:{least}\:{marks}\:{in}\:\mathrm{3}{rd}\:{paper}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{75}+{x};\:\:{x}\in\mathbb{Z} \\ $$$$\mathrm{77}=\mathrm{75}+\mathrm{2} \\ $$$$\mathrm{72}=\mathrm{75}−\mathrm{3} \\ $$$$?\:=\mathrm{75}+{x} \\ $$$$+\mathrm{2}−\mathrm{3}+{x}=\mathrm{0}\Rightarrow{x}=\mathrm{1} \\ $$$$\mathrm{75}+{x}=\mathrm{75}+\mathrm{1}=\mathrm{76} \\ $$

Answered by Rio Michael last updated on 02/Jul/20

Or 75 for 3 papers = 75 × 3 = 225 ⇒ least marks for paper = 225−77−72 = 76 marks

$$\mathrm{Or} \\ $$$$\mathrm{75}\:\mathrm{for}\:\mathrm{3}\:\mathrm{papers}\:=\:\mathrm{75}\:×\:\mathrm{3}\:=\:\mathrm{225} \\ $$$$\Rightarrow\:\:\mathrm{least}\:\mathrm{marks}\:\mathrm{for}\:\mathrm{paper}\:=\:\mathrm{225}−\mathrm{77}−\mathrm{72}\:=\:\mathrm{76}\:\mathrm{marks} \\ $$

Commented by Rasheed.Sindhi last updated on 02/Jul/20

AnOther arithmatic approach.

$${AnOther}\:{arithmatic}\:{approach}. \\ $$

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