Digit and Coin Problems

Systems of EquationsChapter 8

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

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.

Coins

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?

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?

Age Problems

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)