2.14 Solving Word Problems Getting Started!

There’s an amazing fact about a certain number. This fact is called “the four 4’s.” Using the number, you get four different numbers if you add 4, subtract 4, multiply by 4, or divide by 4. When you add all the numbers, you get 60. Is the number 12? Is the number 8? Find the number. Describe how to do it.

Find the number with the four 5’s (add 5, subtract 5, multiply by 5, and divide by 5) that, when you add them together, you get 144.

This puzzle is from a collection created around 500AD. It is about the Greek mathematician Diophantus. His childhood lasted one sixth of his life; he grew a beard after one twelfth more; one seventh later, he got married. Five years later, he had a son. The son lived exactly half as long as his father. Four years after the death of his son, Diophantus died. How old was he? Guess how old he was. Check your guess. Make another guess and check. Write the steps you took to check. Suppose you guess n. How can you check whether n is correct? Find the correct answer – without guessing.

Cameron tells about his trip to the book store. “It was terrible!! They wanted me to join their club to get 10% off. It costs $15 to join the club. It costs $8 more to buy my books if I join the club than if I do not.” How much do the books cost without joining the club?

Are these statements true for some, all, or no numbers? Adding 6 to a number gives the same result as multiplying that number by 3. n+6 = 3n Subtracting 3 from a number gives the same result as adding 3 to that number. 5n – 6 = 3n n – 6 = 34 Doubling a number and then adding 6 gives the same result as adding 3 to a number and then doubling the result. n – 3 = n + 3 Subtracting 5 from a number and then squaring the result gives you 16.

Vanessa works 32 hours a week at her job. Her boss offers her a full- time position (40 hours a week) and a $2 per hour raise. She says, “this is fabulous! Now I’ll make $200 more a week!” What was Vanessa’s hourly wage before the raise?