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This document explores two math problems: the growth rates of two coral colonies and the cost-sharing of snowboarding gear. The coral colonies, initially at 0.17 meters and 0.11 meters, grow at different rates, requiring algebraic modeling to determine when they will be equal in height. The snowboarding gear problem focuses on calculating the price of wax tubes based on combined expenses for goggles and a helmet. Clear equations are set up and solved to find the unknowns, demonstrating practical applications of algebra.

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EXAMPLE 1

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  1. Environment A colony of coral is 0.17 meter high and is growing at a rate of 0.025 meter per year. Another colony is 0.11 meter high and is growing at a rate of 0.041 meter per year. In how many years will the colonies be the same height? Solving an Equation Involving Decimals EXAMPLE 1

  2. Solving an Equation Involving Decimals EXAMPLE 1 SOLUTION First write a verbal model. Let nrepresent the number of years. =

  3. 0.06 0.016x = 0.016 0.016 ANSWER The colonies will be the same height in 3.75 years. Solving an Equation Involving Decimals EXAMPLE 1 0.17 + 0.025n= 0.11 + 0.041n Write algebraic model. 0.17 = 0.11 + 0.016n Subtract 0.025nfrom each side. 0.06 = 0.016n Subtract 0.11 from each side. Divide each side by 0.016 3.75 = n Simplify.

  4. Snowboarding You and a friend are buying snowboarding gear. You buy a pair of goggles that costs $39.95 and 4 tubes of wax. Your friend buys a helmet that costs $54.95 and 2 tubes of wax. You each spend the same amount. Write and solve an equation to find the price of one tube of wax. for Example 1 GUIDED PRACTICE

  5. Let xrepresent the price of one tube of wax. 1. 2x 15.00 = ANSWER 2 2 The price of one tube of wax is $7.50. for Example 1 GUIDED PRACTICE SOLUTION 39.95 + 4x= 54.95 + 2x Write algebraic model. 39.95 + 2x= 54.95 Subtract 2xfrom each side. 2x = 15.00 Subtract 39.95 from each side. Divide each side by 2 x = 7.50 Simplify.

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