Question 418714
Let {{{a}}} = number of 1-point shots made
Let {{{b}}} = number of 2-point shots made
Let {{{c}}} = number of 3-point shots made
given:
(1) {{{1*a + 2*b + 3*c = 96 }}}
(2) {{{a + b + c = 54 }}}
(3) {{{ b = a + 15 }}}
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This is 3 equations and 3 unknowns, so it's solvable
Multiply both sides of (2) by {{{3}}} and 
subtract (1) from (2)
(2) {{{3a + 3b + 3c = 162 }}}
(1) {{{-a - 2b - 3c = -96 }}}
{{{ 2a + b = 66 }}}
Substitute from (3) 
{{{2a + a + 15 = 66}}}
{{{3a = 51}}}
{{{a = 17}}}
and
(3) {{{ b = a + 15 }}}
{{{b = 17 + 15}}}
{{{b = 32}}}
and
(2) {{{a + b + c = 54 }}}
{{{17 + 32 + c = 54}}}
{{{ c = 54 - 49 }}}
{{{c = 5 }}}
The number of 1-point shots made were 17
The number of 2-point shots made were 32
The number of 3-point shots made were 5
check:
(1) {{{1*a + 2*b + 3*c = 96 }}}
(1) {{{17 + 64 + 15 = 96 }}}
{{{ 96 = 96 }}}
OK