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

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

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

Answered by MJS_new last updated on 03/Mar/21

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

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

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

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

$$\left(a\right)$$$$65\mathrm{\%},55\mathrm{\%},45\mathrm{\%},x\mathrm{\%}$$$$average=\frac{65+55+45+x}{4}\mathrm{\%}=\frac{165+x}{4}\mathrm{\%}$$$$50⩽\frac{165+x}{4}⩽60$$$$200⩽165+x⩽240$$$$35⩽x⩽75$$$$i.e.togetCthescoreinfourthtest$$$$mustbebetween35\mathrm{\%}and75\mathrm{\%}.$$$$\left(b\right)$$$$similarly$$$$50⩽\frac{70+60+55+x}{4}⩽60$$$$50⩽\frac{185+x}{4}⩽60$$$$15⩽x⩽55$$$$\left(c\right)$$$$50⩽\frac{60+50+40+x}{4}⩽60$$$$50⩽\frac{150+x}{4}⩽60$$$$50⩽x⩽90$$

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

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

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

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

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