CH 14 ALGEBRA WORD PROBLEMS

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1 85 CH 14 ALGEBRA WORD PROBLEMS Terminology The phrase 7 subtracted from 12 means 12 7, which is 5. To double a number means to multiply the number by 2. Doubling 12 produces 24. [12 2 = 24] To triple a number means to multiply the number by 3. The triple of 10 is 30. [10 3 = 30] To quadruple a number means to multiply the number by 4. When 9 is quadrupled, the result is 36. [9 4 = 36] To quintuple a number means to multiply the number by 5. For instance, when 11 is quintupled, the answer is 55. [11 5 = 55] To square a number means to multiply that number by itself. For example, the square of 7 is 49. [7 7 = 7 2 = 49] Taking the square root of a number is the reverse of squaring. Since 5 squared is 25, we say that the square root of 25 is 5. For a second example, the square root of 144 is this is because 12 squared is 144. [Later in math there will be negative square roots, but in this book, square root means the non-negative square root.] Important Note: Doubling is almost never the same thing as squaring. For example, when 10 is doubled, the result is 20; but when 10 is squared, the result is 100. Actually, there are two numbers for which the double actually does equal the square. One of them is 0, since doubling 0 produces 0 and squaring 0 produces 0. Can you find the other one?

2 86 Homework 1. The following problems will give you practice in basic terminology: a. Calculate 9 subtracted from 20. b. Calculate 200 subtracted from 200. c. Calculate 0 subtracted from 999. d. What is the double of 90? e. What is 33 tripled? f. If 20 is quadrupled, the result is. g. When 25 is quintupled, the answer is. h. The square of 9 is. i. When 25 is squared, the result is. j. What is the square of 16? k. What is the square of 100? l. What is the (positive) square root of 36? m. What is the (positive) square root of 100? n. What is the (positive) square root of 625? Algebra Preview: Doubling x 2x Tripling x 3x Quadrupling x 4x Quintupling x 5x The Square of x is written x 2 The Square Root of x is written x I m Thinking of a Number 2. I'm thinking of a number. If 3 is subtracted from the number, the result is I'm thinking of a number. If my number is subtracted from 2, the result is I'm thinking of a number. If my number is squared, the result is 49.

3 87 5. I'm thinking of a number. If my number is added to 12, the result is I'm thinking of a number. If my number is divided by 9, the result is I'm thinking of a number. If the number is quadrupled, the result is I'm thinking of a number. If 22 is divided by my number, the result is I'm thinking of a number. If the square root of my number is 10, then what is the number? 10. I'm thinking of a number. If the number is multiplied by 9, the result is 0. What is the number? 11. I'm thinking of a number. If the square root of my number is 11, then what is the number? 12. I'm thinking of a number. If the number is tripled, the result is I'm thinking of a number. If my number is subtracted from 21, the result is I'm thinking of a number. If 9 is added to the number, the result is I'm thinking of a number. If my number is squared, the result is I'm thinking of a number. If the number is multiplied by 9, the result is I'm thinking of a number. If 7 is subtracted from the number, the result is I'm thinking of a number. If 16 is divided by my number, the result is I'm thinking of a number. If my number is squared, the result is I'm thinking of a number. If 2 is subtracted from the number, the result is 4.

4 I'm thinking of a number. If my number is divided by 4, the result is I'm thinking of a number. If my number is added to 7, the result is I'm thinking of a number. If my number is subtracted from 2, the result is I'm thinking of a number. If 66 is divided by my number, the result is I'm thinking of a number. If the square root of my number is 12, then what is the number? Coin Problems 26. There are 8 coins, some dimes and some nickels. If the total value of the coins is $0.65, how many of each coin are there? 27. There are 14 coins, some quarters and some pennies. If the total value of the coins is $1.34, how many of each coin are there? 28. There are 10 coins, some dimes and some quarters. If the total value of the coins is $1.45, how many of each coin are there? 29. There are 20 coins, some pennies and some nickels. If the total value of the coins is $0.60, how many of each coin are there? 30. There are 12 coins, some quarters and some nickels. If the total value of the coins is $1.40, how many of each coin are there? Age Problems 31. Joe is 5 times as old as Mike. If Mike is 13, how old is Joe? 32. Sally is twice as old as Martha. If Sally is 64, how old is Martha? 33. Alli s age is the square of Terry s age. If Terry is 9, how old is Alli?

5 John s age is the square of Al s age. If John is 100, how old is Al? 35. Connor is twice as old as Liam. In 4 years Connor will be 10 years older than Liam. How old are Connor and Liam? 36. Moe is currently three times as old as Curly. In 3 years Moe will be twice Curly s age. How old are these guys now? 37. Jason is 15 years older than Stacy. In 5 years Jason will be twice as old as Stacy. How old are Jason and Stacy? 38. Mutt is 3 times as old as Jeff. In 2 years Jeff will be 16 years younger than Mutt. What are Mutt s and Jeff s ages? Solutions 1. a. 11 b. 0 c. 999 d. 180 e. 99 f. 80 g. 125 h. 81 i. 625 j. 256 k. 10,000 l. 6 m. 10 n You should be able to confirm that you have the proper solutions for the coin problems: C:20; L: M:9; C:3 37. J:25; S: M:24; J:8

6 90 It is possible to store the mind with a million facts and still be entirely uneducated. Alec Bourne

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