Question 1026591
Let {{{ n[1] }}} = number of nickels he started with
Let {{{ d[1] }}} = number of dimes he started with
Let {{{ n[2] }}} = number of nickels his mother gave him
Let {{{ d[2] }}} = number of dimes his mother gave him
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(1) {{{ n[1] = d[1] }}}
(2) {{{ 5n[2] + 10d[2] = 400 }}} ( in cents )
(3) {{{ n[1] + n[2] = 2*n[1] }}}
(4) {{{ d[1] + d[2] = 3*d[1] }}}
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There are 4 equations and 4 unknowns, so it's solvable
(3) {{{ n[1] = n[2] }}}
(4) {{{ 2d[1] = d[2] }}}
and
(2) {{{ 5n[2] + 10d[2] = 400 }}}
(2) {{{ 5n[1] + 2*10d[1] = 400 }}}
and, from (1)
(2) {{{ 5d[1] + 2*10d[1] = 400 }}}
(2) {{{ 25d[1] = 400 }}}
(2) {{{ d[1] = 16 }}}
and, from (1),
(2) {{{ n[1] = 16 }}}
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{{{ 5*n[1] + 10*d[1] = 5*16 + 10*16 }}}
{{{ 5*n[1] + 10*d[1] = 80 + 160 }}}
{{{ 5*n[1] + 10*d[1] = 240 }}}
He had 240 cents, or $2.40 to start with
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check:
(3) {{{ n[1] = n[2] }}}
(3) {{{ n[2] = 16 }}}
and
(4) {{{ 2d[1] = d[2] }}}
(4) {{{ 2*16 = d[2] }}}
(4) {{{ d[2] = 32 }}}
and
{{{ 5*n[2] + 10*d[2] = 5*16 +10*32 }}}
{{{ 5*n[2] + 10*d[2] = 80 + 320 }}}
{{{ 5*n[2] + 10*d[2] = 400 }}}
This is correct -his mother gave him $4.00
OK