**Using tools strategically :**

A wide variety of tools are available to help you solve problems. Rulers, models, calculators, protractors, and software are some of the tools you can use in addition to paper and pencil. Choosing tools wisely can help you solve problems and increase your understanding of mathematical concepts.

**Example 1 : **

The depth of Golden Trout Lake has been decreasing in recent years. Two years ago, the depth of the lake was 186.73 meters. Since then the depth has been changing at an average rate of -1 3/4 % per year. What is the depth of the lake today ?

**Solution : **

**Step 1 : **Convert the percent to a decimal

Write the fractional part as a decimal :

-1 3/4% = -1.75%

Move the decimal point two places left.

-1 3/4% = -0.0175

**Step 2 : **

Find the depth of the lake after one year. Use a calculator to simplify the computations.

Find the change in depth :

186.73 × (−0.0175) ≈ −3.27 meters

Find the new depth :

186.73 − 3.27 = 183.46 meters

**Step 3 : **

Find the depth of the lake after two years.

Find the change in depth :

183.46 × (−0.0175) ≈ −3.21 meters

Find the new depth :

183.46 − 3.27 = 180.25 meters

**Step 4 : **

Check the answer for reasonableness.

The original depth was about 190 meters. The depth changed by about −2% per year. Because (−0.02)(190) = −3.8, the depth changed by about −4 meters per year or about −8 meters over two years. So, the new depth was about 182 meters. The answer is close to the estimate, so it is reasonable.

**Example 2 : **

Three years ago, Jolene bought $750 worth of stock in a software company. Since then the value of her purchase has been increasing at an average rate of 12 3/5 % per year. How much is the stock worth now

**Solution : **

**Step 1 : **Convert the percent to a decimal

Write the fractional part as a decimal :

12 3/5% = 12.6%

Move the decimal point two places left.

12 3/5 % = 0.126

**Step 2 : **

Find the change in value after one year. Use a calculator to simplify the computations.

Find the change in value :

750 × (0.126) ≈ $94.5

Find the value after one year :

750 + 94.5 = $844.5

**Step 3 : **

Find the change in price after two years.

Find the change in value :

844.5 × (0.126) ≈ $106.41

Find the value after two years :

844.5 + 106.41 = $950.91

**Step 4 : **

Find the change in price after three years.

Find the change in value :

950.91 × (0.126) ≈ $119.81

Find the value after three years :

950.91 + 119.81 = $1070.72

**Step 5 : **

Check the answer for reasonableness.

Jolene bought $750 worth of stock in a software company. The value of her purchase has been increasing about 13% per year. Because (750)(0.13) = 97.5, the value of the stock changed by about $100 per year or about $300 ( = 100 x 3) over three years. So, the value of the stock after three years is $1050 ( = 750 + 300). The answer is close to the estimate, so it is reasonable.

After having gone through the stuff given above, we hope that the students would have understood "Using tools strategically".

Apart from the stuff given above, if you want to know more about "Using tools strategically", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**