Solve the following problems. Use a table to organize the facts of the problem. See Exampl...

Solve the following problems. Use a table to organize the facts of the problem. See Example.

STATEHOOD From 1800 to 1850, 15 states joined the Union. From 1851 to 1900, an additional 14 states entered. Three states joined from 1901 to 1950. Since then, Alaska and Hawaii are the only others to enter the Union. In all, how many states have joined the Union since 1800?

Example

Orchestras An orchestra consists of a 19-piece woodwind section, a 23-piece brass section, a 54-piece string section, and a two-person percussion section. In all, how many musicians make up the orchestra?

Analyze We can use a table to organize the facts of the problem.

Form In the last sentence of the problem, the phrase in all indicates addition. We translate the words of the verbal model to numbers and symbols.

Calculate We use vertical form to perform the addition:

State There are 98 musicians in the orchestra.

Check To check the addition, we will add upward.

We could also use estimation to check the result. If we front-end round each addend, we get 20 + 20 + 50 + 2 = 92. Since the answer, 98, and the estimate, 92, are close, the result seems reasonable.