Digit and Coin Problems

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Presentation transcript:

Digit and Coin Problems Systems of Equations Chapter 8

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

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

Coins

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 $1.65. 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

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 $1978.75. How many adults and how many children attended? Let a = # of Let c = # of adults children System of Equations a + c = 411 Quantity 5a + 3.75c = 1978.75 Value