Question

A cash register contains only five dollar and ten dollar bills. It contains 24 more five dollar bills than ten dollar bills, and the total amount of money in the cash register is $540. How many of each bill is in the cash register?

Answer 1

`x-\ number\ of\ five\ dollar\ bills\\ y-\ number\ of\ ten\ dollar\ bills\\\\ \left \{ {{x=y+24} \atop {5x+10y=540}} \right. \\\\ substotute\ x=y+24\ to\ the\ second\ equation\\\\ 5(y+24)+10y=540\\\\ 5y+120+10y=540\\\\ 15y+120=540\ \ \ | subtract\ 120\\\\ 15y=420\ \ \ | divide\ by\ 15\\\\ y=28\\\\ x=y+24=28+24=52\\\\ There\ are\ 52\ five\ dollar\ bills\ and\ 28\ ten\ dollar\ bills.`