|
Question 842183: Mr. Ray handed the bank teller a check for $260 and said,"I wish three times as many one-dollars bills as fives, and half as many tens as fives," What should the teller have given him
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! o = number of one dollar bills.
t = number of ten dollar bills.
f = number of five dollar bills.
in terms of dollars.
each one is worth one dollar.
each ten is worth 10 dollars.
each 5 is worth 5 dollars.
in terms of value, then:
o + 5f + 10t = 260 dollars.
that translates to the number of one dollars bills times 1 plus the number of 5 dollars bills times 5 plus the number of 10 dollar bills plus 10 times the number of 10 dollars bills is equal to 260 dollars.
the statement:
"I wish three times as many one-dollars bills as fives, and half as many tens as fives,"
translates to:
o = 3f
this means that the number of one dollar bills is three times the number of five dollar bills.
t = f/2
this means that the number of ten dollar bills is 1/2 times the number of five dollar bills.
start with the general equation of:
o + 5f + 10t = 260
replace o with 3f to get:
3f + 5f + 10t = 260
replace t with f/2 to get:
3f + 5f + 10f/2 = 260.
simplify to get:
3f + 5f + 5f = 260.
combine like terms to get:
13f = 260
divide both sides of the equation by 13 to get:
f = 260 / 13 = 20
since t = f/2, then t = 10
since o = 3f, then o = 60
you get:
o = 60
f = 20
t = 10
the general equation of o + 5f + 10t = 260 becomes:
60 + 5*20 + 10*10 = 260 becomes:
60 + 100 + 100 = 260 which becomes:
260 = 260 which confirms the solutions is good.
you have 60 ones, 20 fives, and 10 tens.
the number of ones is equal to 3 times the number of fives.
the number of tens is equal to 1/2 times the number of fives.
the sum of the dollar value is equal to 260.
|
|
|
| |
