Chapter Eight:  Systems of Equations

Take notes on the following topics.

Chapter Eight

Section 8.1

Section 8.2

Section 8.3

Section 8.4

Section 8.5

Section 8.6

Back to Mrs. Leary's Math Web Page or Back to Algebra Contents

Section 8.6   Digit and Coin Problems 

(Examples provided by Prentice Hall)

 

Example 1		The sum of the digits of a two-digit number is 10. If the digits are reversed, the new number is 36 less than the original number. Find the original number. Let x = the tens digit. Let y = the ones digit. x + y = 10 10x + y – 36 = 10y + x Simplifying, 9x – 9y = 36 Multiplying the first equation by nine to make the y-terms additive inverses, 9x + 9y = 90 9x – 9y = 36 18x = 126 x = 7 Substitute 7 for x in the first equation and solve for y. 7 + y = 10 y = 3 The original number is 73.
Example 2	A collection of nickels and dimes is worth $3.95. There are 8 more dimes than nickels. How many dimes and how many nickels are there? We use dollars as the unit of money. A nickel is worth 0.05 dollars. A dime is worth 0.10 dollars. Let n be the number of nickels. Let d be the number of dimes. 0.05n + 0.10d = 3.95 Multiply by 100 to clear the decimals. 5n + 10d = 395     (1) d = n + 8 (2) Substitute for d in (1). 5n + 10(n + 8) = 395 15n = 315 n = 21 Substitute in (2). d = 29 There are 29 dimes and 21 nickels.
Example 3	A fork and knife weigh 50 grams and 70 grams, respectively. If the set contains 20 knives and forks and weighs 1220 grams, how many knives and forks are there? Let f be the number of forks. Let k be the number of knives. f + k = 20     (1) 50f + 70k = 1220 (2)   Multiply (1) by –50. –50f – 50k = –1000     (1) Add (1) and (2). 20k = 220 k = 11 Substitute in (1). f + 11 = 20 f = 9 There are 9 forks and 11 knives.