Question 775499
Q:
Mary has grades of 98, 76, 86, and 92 on four tests. Within what range must her grade on a fifth test fall if she wishes an average between 80 and 90 on all five tests?
--------------------------------------------------------------------
A:
Let x = Mary's grade on fifth test
Average = {{{(98 + 76 + 86 + 92 + x)/5}}} = {{{(362 + x)/5}}}.
{{{80 <= (352+x)/5 <= 90}}}, multiply both sides by 5
{{{400 <= 352+x <= 450}}}, subtract both sides by 352
{{{400-352 <= x <= 450-352}}}
{{{48 <= x <= 98}}}
Answer: between 48 and 98