SOLUTION: 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

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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.





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