Question

a cashier at the supermarket has $685 in 4 different denomination bills in her register at the end of the day. the number of $5 bills was 10 more than 4 times the amount of $10 bills. the register contained as many $1 bills as $5 bills and $10 bills combined, and two $50 bills. how many bills of each kind did the register contain?

Answer 1

85 ones

70 fives

15 tens

2 fifties

Answer 2

9514 1404 393

Answer:

• 85 ones
• 70 fives
• 15 tens
• 2 fifties

Step-by-step explanation:

Let a, b, c, d represent the numbers of $1, $5, $10, and $50 bills, respectively. The problem statement tells us ...

  a +5b +10c +50d = 685 . . . . . total amount of cash

  b = 10 +4c . . . . . . . . . . . . the number of fives is 10 more than 4 times tens

  a = b+c . . . . . . . . . . . as many ones as fives and tens combined

  d = 2 . . . . . . . . . . the register contained 2 fifty-dollar bills

__

Substituting for 'a', then for 'b', we have ...

  (b+c) +5b +10c +50d = 685

  6(10 +4c) +11c +50d = 685

  60 +35c +50d = 685

Substituting d=2 and subtracting 160 gives ...

  35c = 525

  c = 15

  b = 10 +4c = 10 +4(15) = 70

  a = b+c = 70 +15 = 85

The register contained ...

• 85 ones
• 70 fives
• 15 tens
• 2 fifties