Question

The cash drawer of the market contains $227. There are six more $5 bills than $10 bills. The number of $1 bills is two more than 24 times the number of $10 bills. How many bills of each kind are there?

Answer 1

Step-by-step explanation:

From the information we assume their are 1, 5, and 10 bills (no 20's)

let c = no. of $1 bills

let f = no. of $5

let t = no. of $10

:

Write an equation for each statement:

:

"The cash drawer of the market contains $227 in bills."

1c + 5f + 10t = 227

:

"There are six more $5 bills than $10 bills."

f = t+6

:

"The number of $1 bills is two more than 24 times the number of $10 bills."

c = 24t + 2

:

Use the 1st equation, substitute (t+6) for f, and (24t+2) for c

1(24t+2) + 5(t+6) + 10t = 227

24t + 2 + 5t + 30 + 10t = 227

combine like terms

24t + 5t + 10t + 2 + 30 = 227

39t + 32 = 227

39t = 227 - 32

39t = 195

t = 195%2F39

t = 5 ten dollar bills

:

Find the ones and fives

c = 24t + 2

c = 24(5) + 2

c = 120 + 2

c = 122 one dollar bills

:

f = t + 6

f = 5 + 6

f = 11 five dollar bills

;

:

See if this is true:

1(122) + 5(11) + 10(5) =

122 + 55 + 50 = 227, confirm our solutions

:

HOPE IT HELPS