SOLUTION: Brandon has $140 in his pocket, consisting of $20, $10 and $5 bills. The number of $20 bills is two less than the number of $5 bills. If he has 13 bills in his pocket, how many of
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Question 515516: Brandon has $140 in his pocket, consisting of $20, $10 and $5 bills. The number of $20 bills is two less than the number of $5 bills. If he has 13 bills in his pocket, how many of each denomination does he have?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
x = number of $5 bills
5x = value of the $5 bills in dollars
y = number of $10 bills
10y = value of the $10 bills in dollars
z = number of $20 bills
20z = value of the $20 bills in dollars
.
x + y + z = 13
.
5x + 10y + 20z = 140
.
z = x-2
.
substitute
.
x +y +x-2 = 13
2x +y = 15
.
5x + 10y +20(x-2) = 140
5x +10y +20x -40 = 140
25x +10y= 180
5x +2y = 36
.
2x +y = 15
5x +2y = 36
.
4x +2y = 30
5x +2y = 36
------------
-x = -6
x = 6
.
z = x-2
z = 4
.
x + y + z = 13
6 + y + 4 = 13
y = 3
.
Check values to make sure this is $140
.
5*6 = 30
10*3 = 30
20*4 = 80
30 + 30 + 80 = 140
Correct.
.
Answer: He has 6 $5 bills, 3 $10 bills, and 4 $20 bills.
.
Done.
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