Question 149572
Let's call dimes, D, and quarters, Q.
1.{{{D+Q=28}}} Total number of coins.
2.{{{0.10*D+0.25*Q=4.75}}} Total value of coins.
Let's multiply equation 2 by 100 to get rid of decimals.
1.{{{D+Q=28}}}
2.{{{10D+25Q=475}}}
Use eq. 1 to solve for D and a function of Q.
1.{{{D+Q=28}}}
{{{D=28-Q}}}
Now substitute this expression for D in eq. 2,
2.{{{10D+25Q=475}}}
{{{10(28-Q)+25Q=475}}}
Solve for Q.
{{{280-10Q+25Q=475}}}
{{{280+15Q=475}}}
{{{15Q=195}}}
{{{Q=13}}}
Use eq.1 to solve for D.
{{{D=28-Q}}}
{{{D=28-13}}}
{{{D=15}}}
Audrey has 15 dimes and 13 quarters.