Question 1006951
Let {{{ a }}} = the number of 2-point problems
Let {{{ b }}} = the number of 3-point problems
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(1) {{{ a + b = 25 }}}
(2) {{{ 2a + 3b = 60 }}}
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Multiply both sides of (1) by {{{2}}}
and subtract (1) from (2)
(2) {{{ 2a + 3b = 60 }}}
(1) {{{ -2a - 2b = -50 }}}
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{{{ b = 10 }}}
and
(1) {{{ a + b = 25 }}}
(1) {{{ a + 10 = 25 }}}
(1) {{{ a = 15 }}}
There are 15 2-point problems and
There are 10 3-point problems
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check:
(2) {{{ 2a + 3b = 60 }}}
(2) {{{ 2*15 + 3*10 = 60 }}}
(2) {{{ 30 + 30 = 60 }}}
(2) {{{ 60 = 60 }}}
OK