word problem

Question

A cash register contains only ten dollar and tenty dollar bills. It contains five times as many ten dollar bills as twenty dollar bills and the total amount of money in the cash register is $1,750. How many ten dollar bills are in the cash register?

Answer 1

Let X be the number of $10 bills and J be the number of $20 bills.

I choose these letter for the variables because X is the roman number

for 10 and J is for Jackson, as in President Andrew Jackson, whose image is on the $20 bill.

 

X = 5J <--- 5 times as many $10 bills as $20

 

10X + 20J = 1750  <--- total amount is 1750

 

10(5J) + 20J = 1750  <--- substitutes first equation into second

 

50J + 20J = 1750

 

70J = 1750

 

7J = 175 <--- divides both sides by 10

 

J = 175/7 = 25   (Think 7 quarters = 7 x 25 = 125)

 

There are 25 x $20  +  125 x $10  =

              $500 + $1250 = $1750