20. Marlene works as a cashier at a grocery store. At the end of the day, she has a
total of 125 five-dollar bills and ten-dollar bills. The total value of these bills is $990.
a. Write a system of equations that you can use to find the number of five-dollar
bills and the number of ten-dollars bills. Describe what each variable represents.
b. Solve the system and explain what your solution represents.
Answers
a. The system of equations that you can use to find the number of five-dollar bills and ten-dollar bills is x + y = 125, 5x + 10y = 990
b. The number of five-dollar bills are 52 and ten-dollar bills are 73.
Given:
Marlene works as a cashier at a grocery store. At the end of the day, she has a total of 125, five-dollar bills and ten-dollar bills. The total value of these bills is $990.
To find:
a. Write a system of equations that you can use to find the number of five-dollar bills and the number of ten-dollars bills. Describe what each variable represents.
b. Solve the system and explain what your solution represents.
Solution:
Given the total number of five and ten-dollar bills = 125 dollars
Let x be the number of five dollar bills and y be the ten dollars bills
Total number of bills => x + y = 125 --- (1)
The total value of all bills is $990
As we assumed
Number of five dollar bills = x
=> Value of x five dollar bills = 5 dollar × x = 5x dollars
Number of ten dollar bills = y
=> Value of y ten dollar bills = 10 dollar × x = 10y dollars
Given total value = 990
=> 5x + 10y = 990
Divided by 5 into both sides
=> x + 2y = 198 ----- (2)
Now solve (1) and (2) for x and y values
Do (2) - (1)
=> x + 2y - x - y = 198 - 125
=> y = 73
Substitute y = 73 in (1)
=> x + 73 = 125
=> x = 52
Therefore,
a. The system of equations that you can use to find the number of five-dollar bills and ten-dollar bills is x + y = 125, 5x + 10y = 990
b. The number of five-dollar bills are 52 and ten-dollar bills are 73.
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