Digit and Coin Problems Systems of Equations Chapter 8

Any two digit number can be expressed as 10x + y x represents the tens place and y represents the ones place. 45x=4 and y=510(4) +(5) = 71x=7 and y=110(7) +(1) = x=2 and y=910(2) +(9) =29

Let x = tens place y = ones place x + y = 14 Equation 1 Equation 2 10x + y System of Equations Original Number 10y + x Reverse Number Reversed Number = Original Number y + 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 = 165 Value Quantity System of Equations n = d + 12 nickels Let n = # ofLet 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 c = Value Quantity System of Equations a + c = 411 adults Let a = # ofLet c = # of children 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?

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 + 6 In 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)