1. Digit and Coin Problems
Systems of Equations
Chapter 8

2. 10x + y 45 x=4 and y=5 10(4) +(5) = 45 71 x=7 and y=1 10(7) +(1) = 71
Any two digit number can be expressed as
10x + y
x represents the tens place and
y represents the ones place. 45
x=4 and y=5
10(4) +(5) = 45 71
x=7 and y=1
10(7) +(1) = 71 29
x=2 and y=9
10(2) +(9) = 29

3. Find the original number.
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.
Let x = tens place
y = ones place
System of Equations
x + y = 14
Equation 1
Original Number
9x - y = -36
Equation 2
10x + y = 14
Reverse Number
Reversed Number = Original Number + 36
10y + x = 14
10y + x =
36 +
10x + y

4. Coins

5. Kami has some nickels and some dimes. The value of the coins is $1. 65
Kami has some nickels and some dimes. The value of the coins is $ There are 12 more nickels than dimes. How many of each kind of coin
nickels
dimes
Let n = # of
Let d = # of
System of Equations
5n + 10d = 165
Value
n = d + 12
Quantity

6. There were 411 people at a play. Admission was $5 for adults and $3
There were 411 people at a play. Admission was $5 for adults and $3.75 for children. The receipts were $ How many adults and how many children attended?
Let a = # of
Let c = # of
adults
children
System of Equations
a + c = 411
Quantity
5a c =
Value