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Question Number 134383 by otchereabdullai@gmail.com last updated on 03/Mar/21

In a course a student gets grade C if his average in four test is between 50 and 60. Find the range of score X on the fourth test to ensure a grade C given that: (a) A student scores 65% , 55%, and 45% in the first three test. (b) A student score 70%, 60% and 55% on the first three test. (c) A student score 60% , 50% and 40% of the first three test. ase how do we solve such question I need help

$$\mathrm{In}\:\mathrm{a}\:\mathrm{course}\:\mathrm{a}\:\mathrm{student}\:\mathrm{gets}\:\mathrm{grade}\:\mathrm{C}\:\:\mathrm{if} \\ $$$$\mathrm{his}\:\mathrm{average}\:\mathrm{in}\:\:\mathrm{four}\:\mathrm{test}\:\mathrm{is}\:\mathrm{between}\: \\ $$$$\mathrm{50}\:\mathrm{and}\:\mathrm{60}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{score}\:\mathrm{X} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{fourth}\:\mathrm{test}\:\mathrm{to}\:\mathrm{ensure}\:\mathrm{a}\:\mathrm{grade}\:\mathrm{C} \\ $$$$\mathrm{given}\:\mathrm{that}: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{A}\:\mathrm{student}\:\mathrm{scores}\:\mathrm{65\%}\:,\:\mathrm{55\%},\:\mathrm{and} \\ $$$$\:\mathrm{45\%}\:\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{three}\:\mathrm{test}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{A}\:\mathrm{student}\:\mathrm{score}\:\mathrm{70\%},\:\mathrm{60\%}\:\mathrm{and} \\ $$$$\mathrm{55\%}\:\mathrm{on}\:\mathrm{the}\:\mathrm{first}\:\mathrm{three}\:\mathrm{test}. \\ $$$$\left(\mathrm{c}\right)\:\mathrm{A}\:\mathrm{student}\:\mathrm{score}\:\mathrm{60\%}\:,\:\mathrm{50\%}\:\mathrm{and} \\ $$$$\mathrm{40\%}\:\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{three}\:\mathrm{test}. \\ $$$$\mathrm{ase}\:\mathrm{how}\:\mathrm{do}\:\mathrm{we}\:\mathrm{solve}\:\mathrm{such}\:\mathrm{question} \\ $$$$\mathrm{I}\:\mathrm{need}\:\mathrm{help} \\ $$

Answered by MJS_new last updated on 03/Mar/21

total score after 4 tests =((45+55+65+x)/4) 50<((165+x)/4)<60 200<165+x<240 35<x<75

$$\mathrm{total}\:\mathrm{score}\:\mathrm{after}\:\mathrm{4}\:\mathrm{tests}\:=\frac{\mathrm{45}+\mathrm{55}+\mathrm{65}+{x}}{\mathrm{4}} \\ $$$$\mathrm{50}<\frac{\mathrm{165}+{x}}{\mathrm{4}}<\mathrm{60} \\ $$$$\mathrm{200}<\mathrm{165}+{x}<\mathrm{240} \\ $$$$\mathrm{35}<{x}<\mathrm{75} \\ $$

Commented by otchereabdullai@gmail.com last updated on 03/Mar/21

May the almighty Allah give your heart desire! Amen

$$\mathrm{May}\:\mathrm{the}\:\mathrm{almighty}\:\mathrm{Allah}\:\mathrm{give}\:\mathrm{your}\:\mathrm{heart}\: \\ $$$$\mathrm{desire}!\:\mathrm{Amen} \\ $$

Answered by mr W last updated on 03/Mar/21

(a) 65%,55%,45%,x% average=((65+55+45+x)/4)%=((165+x)/4)% 50≤((165+x)/4)≤60 200≤165+x≤240 35≤x≤75 i.e. to get C the score in fourth test must be between 35% and 75%. (b) similarly 50≤((70+60+55+x)/4)≤60 50≤((185+x)/4)≤60 15≤x≤55 (c) 50≤((60+50+40+x)/4)≤60 50≤((150+x)/4)≤60 50≤x≤90

$$\left({a}\right) \\ $$$$\mathrm{65\%},\mathrm{55\%},\mathrm{45\%},{x\%}\: \\ $$$${average}=\frac{\mathrm{65}+\mathrm{55}+\mathrm{45}+{x}}{\mathrm{4}}\%=\frac{\mathrm{165}+{x}}{\mathrm{4}}\% \\ $$$$\mathrm{50}\leqslant\frac{\mathrm{165}+{x}}{\mathrm{4}}\leqslant\mathrm{60} \\ $$$$\mathrm{200}\leqslant\mathrm{165}+{x}\leqslant\mathrm{240} \\ $$$$\mathrm{35}\leqslant{x}\leqslant\mathrm{75} \\ $$$${i}.{e}.\:{to}\:{get}\:{C}\:{the}\:{score}\:{in}\:{fourth}\:{test} \\ $$$${must}\:{be}\:{between}\:\mathrm{35\%}\:{and}\:\mathrm{75\%}. \\ $$$$\left({b}\right) \\ $$$${similarly} \\ $$$$\mathrm{50}\leqslant\frac{\mathrm{70}+\mathrm{60}+\mathrm{55}+{x}}{\mathrm{4}}\leqslant\mathrm{60} \\ $$$$\mathrm{50}\leqslant\frac{\mathrm{185}+{x}}{\mathrm{4}}\leqslant\mathrm{60} \\ $$$$\mathrm{15}\leqslant{x}\leqslant\mathrm{55} \\ $$$$\left({c}\right) \\ $$$$\mathrm{50}\leqslant\frac{\mathrm{60}+\mathrm{50}+\mathrm{40}+{x}}{\mathrm{4}}\leqslant\mathrm{60} \\ $$$$\mathrm{50}\leqslant\frac{\mathrm{150}+{x}}{\mathrm{4}}\leqslant\mathrm{60} \\ $$$$\mathrm{50}\leqslant{x}\leqslant\mathrm{90} \\ $$

Commented by otchereabdullai@gmail.com last updated on 03/Mar/21

May the aAlmigthy Allah give your heart desire! Amen

$$\mathrm{May}\:\mathrm{the}\:\mathrm{aAlmigthy}\:\mathrm{Allah}\:\mathrm{give}\:\mathrm{your}\: \\ $$$$\mathrm{heart}\:\mathrm{desire}!\:\mathrm{Amen} \\ $$$$ \\ $$

Commented by otchereabdullai@gmail.com last updated on 03/Mar/21

i have now seen how to approach such questions thanks a lot prof W and prof mjs

$$\mathrm{i}\:\mathrm{have}\:\mathrm{now}\:\mathrm{seen}\:\mathrm{how}\:\mathrm{to}\:\mathrm{approach}\:\mathrm{such} \\ $$$$\mathrm{questions}\:\mathrm{thanks}\:\mathrm{a}\:\mathrm{lot}\:\mathrm{prof}\:\mathrm{W}\:\mathrm{and}\:\mathrm{prof} \\ $$$$\mathrm{mjs} \\ $$

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