SOLUTION: Phillip has $1,560 in 20-dollar, 50-dollar and 100-dollar bills. If he has twice as many 100-dollar bills as 50-dollar bills,and twice as many 50-dollar bills as 20-dollar bills, h

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Question 1154071: Phillip has $1,560 in 20-dollar, 50-dollar and 100-dollar bills. If he has twice as many 100-dollar bills as 50-dollar bills,and twice as many 50-dollar bills as 20-dollar bills, how many bills does Phillip have in total?
Found 3 solutions by ikleyn, josmiceli, MathTherapy:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x = # of the 20-dollar bills Philip has.


Then the number of 50-dollar bills is 2x, and the number of the 100-dollar bills is 2*(2x) = 4x.


Then the total money is  20x + 50*(2x) + 100*(4x) = (20+100+400)x = 520x dollars,

and it is equal to 1560 dollars, according to the condition.


    520x = 1560

   
Hence, x = 1560/520 = 3.


Thus, there are 3 20-dollar bills,  6 50-dollar bills and 12 100-dollar bills.


In all, there are 3+6+12 = 21 bills.      ANSWER.  

Solved.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of $20 bills
Let +b+ = number of $50 bills
Let +c+ = number of $100 bills
----------------------------------------
(1) +20a+%2B+50b+%2B+100c+=+1560+
(2) +c+=+2b+
(3) +b+=+2a+
----------------------
There are 3 equations & 3 unknowns, so
it's solvable
(3) +a+=+%281%2F2%29%2Ab+
and
(1) +20a+%2B+50b+%2B+100c+=+1560+
(1) +20%2A%281%2F2%29%2Ab+%2B+50b+%2B+100%2A2b+=+1560+
(1) +10b+%2B+50b+%2B+200b+=+1560+
(1) +260b+=+1560+
(1) +b+=+6+
---------------------
(3) +a+=+%281%2F2%29%2Ab+
(3) +a+=+%281%2F2%29%2A6+
(3) +a+=+3+
---------------------
(2) +c+=+2b+
(2) +c+=+2%2A6+
(2) +c+=+12+
---------------------
+a+%2B+b+%2B+c+=+3+%2B+6+%2B+12+
+a+%2B+b+%2B+c+=+21+
Philip has 21 bills
--------------------------
check:
(1) +20a+%2B+50b+%2B+100c+=+1560+
(1) +20%2A3+%2B+50%2A6+%2B+100%2A12+=+1560+
(1) +60+%2B+300+%2B+1200+=+1560+
(1) +1560+=+1560+
OK

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Phillip has $1,560 in 20-dollar, 50-dollar and 100-dollar bills. If he has twice as many 100-dollar bills as 50-dollar bills,and twice as many 50-dollar bills as 20-dollar bills, how many bills does Phillip have in total?
Let the number of $20 bills be T
Then the number of $50 bills = 2T
Also, the number of $100 bills = 2(2T) = 4T
We then get: 20T + 50(2T) + 100(4T) = 1,560
20T + 100T + 400T = 1,560
520T = 1,560
T, or

You should now be able to find the total number of bills!