It's that time again, folks!
Rough Guide for Solving Word Problems :
- Step 1. Read the problem carefully to determine what you are being asked to find.
- Step 2. Select a variable to represent each unknown quantity. Specify precisely what each variable represents and note any restrictions on each variable.
- Step 3. If necessary, make a sketch and translate the problem into a word equation or a system of word equations. Then translate each word equation into an algebraic equation.
- Step 4. Solve the equation or system of equations, and answer the question completely in the form of a sentence.
- Step 5. Check the reasonableness of your answer.
A Unifying Principle: The Mixture Principle
Mixture Principle for Two Ingredients:
Amount Stuff in First + Amount Stuff in Second=Amount Stuff in Mixture
Another Classic Mixture Problem: A goldsmith named would like to make 75 g of a gold alloy which is 72% gold. How much of an alloy which is 86% gold, and another alloy which is 56% gold, should the goldsmith use? Round your answer to the nearest gram.
Example: $I=Prt$
made an investment of $\$$11000. One part of the investment went into a bond fund which paid a rate of 6 percent per year, and the rest of the investment went into stocks which earn interest at a rate of 8 percent per year. The combined interest earned at the end of 1 year was $\$$764. How much was invested at each rate?
Example: $D=RT$
A jet plane and a refueling plane that are 675 mi apart head toward each other so that the jet can refuel. The jet flies 250 mi/h faster than the tanker. Determine the speed of each aircraft if they meet in 40 minutes. Round your answer to the nearest mile per hour.
Caution: be careful with units.
Bonus Example: $W=RT$
A small building contractor plans to add a bricklayer to his full-time crew. He has two bricklayers on a current job that he is considering for this position. On Monday, he observed that these two bricklayers each worked 7 hours and laid a total of 3455 bricks. On Tuesday, the older bricklayer worked 9 hours, the younger bricklayer worked 6 hours, and they laid a total of 3568 bricks. Determine for the contractor the rate of work for each bricklayer, assuming that both bricklayers work at a fairly consistent rate. Round your answer to the nearest brick per hour.