Question 962211
Let {{{ a }}} = number of students in 2nd period class
Let {{{ s }}} = sum of the scores for the 1st period class
Let {{{ t }}} = sum of the scores for the 2nd period class
For 2nd period class:
(1) {{{ t / a = .8 }}}
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For 1st period class:
(2) {{{ s / 23 = .91 }}}
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(3) {{{ ( s + t ) / ( a + 23 ) = .846 }}}
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There are 3 equations and 3 unknowns, so it's solvable
(2) {{{ s = .91*23 }}}
(2) {{{ s = 20.93 }}}
and
(1) {{{ t = .8a }}}
and
(3) {{{ ( s + t ) / ( a + 23 ) = .846 }}}
(3) {{{ ( 20.93 + .8a ) / ( a + 23 ) = .846 }}}
(3) {{{ 20.93 + .8a = .846*( a + 23 ) }}}
(3) {{{ 20.93 + .8a = .846a + 19.458 }}}
(3) {{{ .046a = 20.93 - 19.458 }}}
(3) {{{ .046a = 1.472 }}}
(3) {{{ a = 32 }}}
and
(1) {{{ t = .8a }}}
(1) {{{ t = .8*32 }}}
(1) {{{ t = 25.6 }}}
and
There are 32 students in the 2nd period class
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check:
Total number of students =
{{{ 23 + 32 = 55 }}}
Average for total = {{{ .846 }}}
{{{ x / 55 = .846 }}}
{{{ x = 46.53 }}}
{{{ x = s + t }}}
{{{ x = 20.93 + 25.6 }}}
{{{ x = 46.53 }}}
{{{ 46.53 / 55 = .846 }}}
OK