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Solving Math Problems with Coin Values and Investment Interest

This document presents three engaging examples of solving practical mathematical problems. The first example involves a coin bank holding nickels, dimes, and quarters, requiring the use of substitution to find the quantity of each type of coin given certain conditions. The second example illustrates John's investment in three mutual funds and calculates the amounts invested at various interest rates. Lastly, the third example deals with finding a three-digit number based on specific digit-related conditions. Each problem emphasizes problem-solving strategies and systems of equations.

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Solving Math Problems with Coin Values and Investment Interest

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  1. Section 3.4 Applications

  2. Example 1 • A coin bank holds nickels, dimes, and quarters. There are 45 coins in the bank and the value of the coins is $4.75. If there are five more nickels than quarters, find the number of each type of coin in the bank.

  3. N = # of nickels • D = # of dimes • Q = # of quarters • We will use substitution to solve the 1st part of this problem.

  4. There are 10 nickels, 30 dimes, and 5 quarters.

  5. Example 2 • John invested $6500 in three different mutual funds for one year. He earned a total of $560 in simple interest on the three investments. The first fund paid 5% interest, and the second fund paid 8% interest, and the third fund paid 10% interest. If the sum of the first two investments was $500 less than the amount of the third investment, find the amount he invested at each rate.

  6. x = amount invested in 5% fund • y = amount invested in 8% fund • z = amount invested in 10% fund

  7. John invested $1000 at 5%, $2000 at 8%, and $3500 at 10%.

  8. Example 3 • The sum of the digits of a three digit number is 12. Five times the units digit plus 6 times the tens digit is 28. If 2 times the tens digit is subtracted from 3 times the hundreds digit, the result is 15. Find the number.

  9. U = the units digit • T = the tens digit • H = the hundred digit

  10. The number is 732.

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