Digit and Coin Problems Systems of Equations Chapter 8.
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Transcript of Digit and Coin Problems Systems of Equations Chapter 8.
![Page 1: Digit and Coin Problems Systems of Equations Chapter 8.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649cf55503460f949c4bbf/html5/thumbnails/1.jpg)
Digit and Coin Problems
Systems of EquationsChapter 8
![Page 2: Digit and Coin Problems Systems of Equations Chapter 8.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649cf55503460f949c4bbf/html5/thumbnails/2.jpg)
Any two digit number can be expressed as
10x + yx represents the tens place and
y represents the ones place.
45 x=4 and y=5 10(4) +(5) =
71 x=7 and y=1 10(7) +(1) =
45
71
29 x=2 and y=9 10(2) +(9) = 29
![Page 3: Digit and Coin Problems Systems of Equations Chapter 8.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649cf55503460f949c4bbf/html5/thumbnails/3.jpg)
Let x = tens place y = ones place
x + y = 14Equation 1
Equation 210x + y
System of Equations
Original Number
10y + x Reverse Number Reversed Number = Original Number + 36
10y + x = 10x + y36 +
9x - y = -36
The sum of the digits of a two digit number is 14. If the digits are reversed, the number is 36 greater than the original number.
Find the original number.
![Page 4: Digit and Coin Problems Systems of Equations Chapter 8.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649cf55503460f949c4bbf/html5/thumbnails/4.jpg)
Coins
![Page 5: Digit and Coin Problems Systems of Equations Chapter 8.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649cf55503460f949c4bbf/html5/thumbnails/5.jpg)
5n + 10d = 165Value
Quantity
System of Equations
n = d + 12
nickelsLet n = # of Let d = # of
dimes
Kami has some nickels and some dimes. The value of the coins is $1.65. There are 12 more nickels than dimes. How many of each kind of coin does Kami have?
![Page 6: Digit and Coin Problems Systems of Equations Chapter 8.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649cf55503460f949c4bbf/html5/thumbnails/6.jpg)
5a + 3.75c = 1978.75Value
Quantity
System of Equations
a + c = 411
adultsLet a = # of Let c = # of
children
There were 411 people at a play. Admission was $5 for adults and $3.75 for children. The receipts were $1978.75. How many adults and how many children attended?
![Page 7: Digit and Coin Problems Systems of Equations Chapter 8.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649cf55503460f949c4bbf/html5/thumbnails/7.jpg)
Age Problems
![Page 8: Digit and Coin Problems Systems of Equations Chapter 8.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649cf55503460f949c4bbf/html5/thumbnails/8.jpg)
Let y = Laura’s ageLet x = Shirley’s age
x + 6 = Shirley’s age in six years
y + 6 = Laura’s age in six years
x = 2y + 6In 6 years
Now
System of Equations
x = y + 21
Shirley is 21 years older than Laura. In six years, Shirley will be twice as old as Laura. How old are they now?
x + 6 =Shirley in 6 years = 2 (Laura in 6 years)
2 (y + 6)