Question 408137
{{{t}}} = number of $10 bills
{{{f}}} = number of $5 bills
{{{n}}} = number of $1 bills
given:
(1) {{{10t + 5f + 1n = 446}}}
(2) {{{t + f + n = 94}}}
(3) {{{f = t + 10}}}
There are 3 equations and 3 unknowns,
so it's solvable
Subtract (2) from (1)
(1) {{{10t + 5f + 1n = 446}}}
(2) {{{-t - f - n = -94}}}
{{{9t + 4f = 352}}}
Substitute (3) into the result
{{{9t + 4*(t + 10) = 352}}}
{{{9t + 4t + 40 = 352}}}
{{{13t = 312}}}
{{{t = 24}}}
and, since
{{{f = t + 10}}}
{{{f = 34}}}
and
(2) {{{t + f + n = 94}}}
{{{24 + 34 + n = 94}}}
{{{n= 94 - 58}}}
{{{n = 36}}}
Andrew had 36 $1 bills
check answer:
(1) {{{10t + 5f + 1n = 446}}}
(1) {{{10*24 + 5*34 + 1*36 = 446}}}
{{{240 + 170 + 36 = 446}}}
{{{446 = 446}}}
OK