8-6 Digit and Value (Money)

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Presentation transcript:

8-6 Digit and Value (Money) Assignment: 8-6/1-13 odd, 25-41 odd

Value problems (already have done many of these in (8-4) One equation: Quantity (number of items) Other equation: Value (Cost, weight, etc) Digit Problems Any two digit number can be expressed as 10x + y ( 52: 10*5 + 2 so x =5 and y = 2) The reverse would become 10y + x (10*2 + 5 or 25)

That means 350 adults attended Example 1: There were 411 people at a play. Admission was $1.00 for adults and 75¢ for children. The receipts were for $395.75. How many children attended? Quantity: a + c = 411 Value: 1a + 0.75c = 395.75 a + c = 411 ( ) -1 + -1a - 0.75c = -395.75 0.25c = 15.25 c = 61 61 children attended That means 350 adults attended

That’s the nickels. Now the dimes Example 2: Calvin paid his skate rental of $1.35 with nickels and dimes. There were 19 coins. How many of each coin did he have? Quantity: x + y = 19 Value: 0.05x + 0.10y = 1.35 -0.10x + -0.10y = -1.9 ( )-0.10 + 0.05x + 0.10y = 1.35 -0.05x = -0.55 11 + y = 19 y = 8 There were 8 dimes x = 11 That’s the nickels. Now the dimes

Substitution will work here Example 3: The sum of the digits of a two-digit number is 14. If the digits are reversed, The new number is 36 greater than the original number. Find the original number. Substitution will work here y =14 - x 1st: x + y =14 2nd: 10y + x = 10x +y +36 5 + y = 14 y = 9 The number is 59 10(14 - x) + x =10x + 14 - x + 36 140 -10x + x = 50 + 9x 140 – 9x = 50 + 9x 90 =18x 5 = x

Lets use elimination this time. Example 4: If 27 is added to a two digit number, the result is a number with the same digits, but in reverse order. The sum of the digits are 11. What is the original number? 1st: 10x + y +27 = 10y + x 2nd: x + y = 11 Lets use elimination this time. 9x - 9y = -27 ( ) 9 + 9x + 9y = 99 18x = 72 x = 4 4 + y =11 y = 7 The number is 47

Assignment