Question 196511
Let {{{a}}}= the number of $1 coins she has
Let {{{b}}}= the number of $2 coins she has
given:
{{{a + b = 37}}}
{{{1*a + 2*b = 51}}}
Subtract the 1st equation from the 2nd
{{{1*a + 2*b = 51}}}
{{{-a - b = -37}}}
{{{b = 14}}}
And, since
{{{a + b = 37}}}
{{{a + 14 = 37}}}
{{{a = 37 - 14}}}
{{{a = 23}}}
She has 23 $1 coins and 14 $2 coins
check:
{{{a + b = 37}}}
{{{23 + 14 = 37}}}
{{{37 = 37}}}
OK
{{{a + 2b = 51}}}
{{{23 + 28 = 51}}}
{{{51 = 51}}}
OK