Question 527491
Let {{{a}}} = number of correct solutions
Let {{{b}}} = number of incorrect solutions
given:
(1) {{{ 8a - 5b = 0 }}}
(2) {{{ a + b = 26 }}}
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Multiply both sides of (2) by {{{5}}}
and add the equations
(1) {{{ 8a - 5b = 0 }}}
(2) {{{ 5a + 5b = 130 }}}
{{{ 13a = 130 }}}
{{{ a = 10 }}}
and, since
(2) {{{ a + b = 26 }}}
(2) {{{ 10 + b = 26 }}}
(2) {{{ b = 16 }}}
The daughter solved 10 equations correctly
check:
(1) {{{ 8a - 5b = 0 }}}
(1) {{{ 8*10 - 5*16 = 0 }}}
(1) {{{ 80  - 80 = 0 }}}
{{{ 0 = 0 }}}
OK