Question

Hannah has a jar filled with 150 coins made up of quarters and nickels. The total value of the coins is $28.30 How many quarters and how many nickels are in the jar? a. 46 quarters; 104 nickels b. 75 quarters; 75 nickels c. 104 quarters; 46 nickels d. 95 quarters; 55 nickels

Answer 1

$x-number\ of\ nickels\\y-number\ of\ quarters\\\\ \left \{ {{x+y=150} \atop {0.05x+0.25y=28.3}} \right. \\\\From\ first\ equation:\\x=150-y\\\\Substiute\ to\ second:\\0.05(150-y)+0.25y=28.3\\7.5-0.05y+0.25y=28.3\\-0.05y+0.25y=28.3-7.5\\0.2y=20.8\ \ \ \ |:0.2\\y=104\\\\x=150-104=46\\\\Answer\ c.$

Answer 2

The correct answer is c. because 104 times 25 is 2600 and 46 times 5 is 230. All you do is put in the decimals :)