Question 579126
Let {{{ a }}} = number of 2-point questions
Let {{{ b }}} = number of 5-point questions
given:
(1) {{{ a + b = 38 }}}
(2) {{{ 2a + 5b = 100 }}}
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Multiply both sides of (1) by {{{2}}}
and subtract (1) from (2)
(2) {{{ 2a + 5b = 100 }}}
(1) {{{ -2a - 2b = -76 }}}
{{{ 3b = 24 }}}
{{{ b = 8 }}}
and, since
(1) {{{ a + 8 = 38 }}}
(1) {{{ a = 30 }}}
There are 30 of the 2-point questions
There are 8 of the 5-point questions
check:
(2) {{{ 2*30 + 5*8 = 100 }}}
(2) {{{ 60 + 40 = 100 }}}
(2) {{{ 100 = 100 }}}
OK