Question

A stack of​ $20, $50, and​ $100 bills was retrieved as part of a police investigation. There were 42 42 more​ $50 bills than​ $100 bills.​ Also, the number of​ $20 bills was 7 7 times the number of​ $100 bills. If the total value of the money was ​$ 9930 9930​, find the number of each type of bill. The number of​ $100 bills was nothing . The number of​ $50 bills was nothing . The number of​ $20 bills was nothing . Enter your answer in each of the answer boxes.

Answer 1

Answer:

The number of​ $100 bills was 27.

The number of​ $50 bills was 69.

The number of​ $20 bills was 189.

Step-by-step explanation:

Let x be the number of $20 bills, y the number of $50 bills, and z the number of $100 bills.

Since there are three unknown values, we need three equations to solve the problem, all of them can be extracted from the question itself, two as the ratios between different bills and the last one as the sum of the total value of the money :

$y=z+42\\x=7*z\\20x+50y+100z = 9,930$

Substituting the first equations into the last, it is possible to find the value for z:

$20(7z)+50(z+42)+100z = 9,930\\z=\frac{9,930-2100}{290} \\z=27$

Knowing that there were 27 $100 bills, we can go back to the first two equations to find x and y:

$y=z+42=27+42\\y= 69\\x=7*z=7*27\\x= 189$

The number of​ $100 bills was 27.

The number of​ $50 bills was 69.

The number of​ $20 bills was 189.