Question 214173
Let {{{n}}} = number of quarters
Let {{{q}}} = number of quarters
given:
(1) {{{n + q = 142}}}
(2) {{{5n + 25q = 1530}}} (in cents)
Multiply both sides of (1) by {{{5}}}, and
subtract (1) from (2)
(2) {{{5n + 25q = 1530}}}
(1) {{{-5n - 5q = -710}}}
{{{20q = 820}}}
{{{q = 41}}}
and, since
{{{n + q = 142}}}
{{{n + 41 = 142}}}
{{{n = 101}}}
Hae has 41 quarters and 101 nickels
check answer:
(2) {{{5n + 25q = 1530}}}
{{{5*101 + 25*41 = 1530}}}
{{{505 + 1025 = 1530}}}
{{{1530 = 1530}}}
OK