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Chapter 1: Problem 53
What is estimation? When is it helpful to use estimation?
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Obtain an estimate for each computation by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head. Then use a calculator to perform the computation. How reasonable is your estimate when compared to the actual answer? \(248+797\)
Use inductive reasoning to predict the next line in each sequence of computations. Then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct. $$ \begin{aligned} 1 \times 9-1 &=8 \\ 21 \times 9-1 &=188 \\ 321 \times 9-1 &=2888 \\ 4321 \times 9-1 &=38,888 \end{aligned} $$
Use Polya's four-step method in problem solving to solve Exercises 9-40. a. Which is the better value: a 15.3-ounce box of cereal for \(\$ 3.37\) or a 24 -ounce box of cereal for \(\$ 4.59\) ? b. The supermarket displays the unit price for the 15.3-ounce box in terms of cost per ounce, but displays the unit price for the 24-ounce box in terms of cost per pound. What are the unit prices, to the nearest cent, given by the supermarket? c. Based on your work in parts (a) and (b), does the better value always have the lower displayed unit price? Explain your answer.
The Republic of Margaritaville is composed of four states: A, B, C, and D. According to the country's constitution, the congress will have 30 seats, divided among the four states according to their respective populations. The table shows each state's population. $$ \begin{aligned} &\text { POPULATION OF MARGARITAVILLE BY STATE }\\\ &\begin{array}{|l|l|l|l|l|l|} \hline \text { State } & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\ \hline \begin{array}{l} \text { Population } \\ \text { (in thousands) } \end{array} & 275 & 383 & 465 & 767 & 1890 \\ \hline \end{array} \end{aligned} $$ Allocate the 30 congressional seats among the four states in a fair manner.
Determine each estimate without using a calculator. Then use a calculator to perform the computation necessary to obtain an exact answer. How reasonable is your estimate when compared to the actual answer? You lease a car at \(\$ 605\) per month for 3 years. Estimate the total cost of the lease.
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