Question 497536
Let {{{a}}} = number of share of stock A she owns
Let {{{b}}} = number of share of stock B she owns
Let {{{c}}} = number of share of stock C she owns
given:
(1) {{{ b = a/2 }}}
(2) {{{ c = b/2 }}}
(3) {{{ 4.5a + 7b + 10c = 546 }}}
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This is 3 equations and 3 unknowns, so it's solvable
(1) {{{ b = a/2 }}}
(1) {{{ a = 2b }}}
Substitute (1) and (2) into (3)
(3) {{{ 4.5a + 7b + 10c = 546 }}}
(3) {{{ 4.5*2b + 7b + 10*(b/2) = 546 }}}
(3) {{{ 9b + 7b + 5b = 546 }}}
(3) {{{ 21b = 546 }}}
{{{ b = 26 }}}
and, since
(1) {{{ a = 2b }}}
(1) {{{ a = 52 }}}
also,
(2) {{{ c = b/2 }}}
(2) {{{ c = 13 }}}
She owns 52 shares of A, 26 shares of B, and
13 shares of C
check answer:
(3) {{{ 4.5*52 + 7*26 + 10*13 = 546 }}}
(3) {{{ 234 + 182 + 130 = 546 }}}
(3) {{{ 546 = 546 }}}
OK