Equations Involving Decimals and Problem Solving
When we have linear equations with decimals we first take steps to transform the equation into one without decimals.
To do this:
1. Look at all the constants and coefficients in the problem and see how many decimal places they have
2. We multiply each term in the equation by the number that eliminates all the decimals.
For example multiply by 10 if you have some numbers with one decimal place, multiply by 100 if you have some numbers with two decimal places, etc.
Make sure that you multiply all terms by the same number and that you multiply by the number that eliminates ALL the decimals.
This will change the equation into one without decimals and we can solve it with the usual methods.
To see some examples of how this is done, click on the word "Example":Example 1: Solve 0.2x + 0.24 = 0.08x + 0.72
Example 2: Solve 0.07x + 0.11x = 3.6
Example 3: Solve s = 1.95 + 0.35s
Example 4: Solve 0.12x + 0.11(7000 – x) = 790
Word Problems:
In order to solve work problems of this type it is helpful to use the following steps:
1. Read through the problem carefully and identify what you are trying to find. This is the unknown.
2. Assign a letter to the unknown. For example x = unknown quantity.
3. Read through the problem again and write an equation for x.
4. Solve the equation using the methods for solving linear equations.
To see some examples of how this is done, click on the word "Example":
Example 5: Karyl bought a dress at a 35% discount sale for $32.50. What was the original price of the dress?
Example 6: A pair of jogging shoes that was originally priced at $50 is on sale for 20% off. Find the discount sale price of the shoes.
Example 7: A retailer has some shirts that cost $20 each. She wants to sell them at a profit of 60% of the cost. What selling price should be marked on the shirts?
Example 8: A retailer of sporting goods bought a putter for $18. He wants to price the putter such that he will make a profit of 49% of the selling price. What price should he mark on the putter?
Example 9: If a maple tree costs a landscaper $55.00, and he sells it for $80.00, what is his rate of profit based on the cost? Round the rate to the nearest tenth of a percent.
Example 10: Erick has 40 coins, consists only of dimes and nickels, worth $3.35. How many dimes and how many nickels does he have?
Example 11: A man invests $8000, part of it at 11% and the remainder at 12%. His total yearly interest from the two investments is $930. How much did he invest at each rate?