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Setting up Algebra Word Problems Double Jake’s age, x, minus 4 is 22 2x – 4 = 22 How to start a word problem 1. Read the problem all the way through quickly to see what kind of word problem it is and what it is about. 2. Look for a question at the end of the problem. This is often a good way to find what you are solving for. Sometimes two or three things need to be found. 3. What you are trying to find is usually stated in the question at the end of the problem. 4. Read the problem again. This time read it one piece at a time. Simple problems usually have two unknowns, and the other gives you equation information. Translate the problem from words to symbols one piece at a time. Common Statements and the Algebra Representation Statement Algebra Twice as much as the unknown 2x Two less than the unknown x-2 Five more than the unknown x+5 Three more than twice the unknown 2x + 3 a number decreased by 7 ten decreased by the unknown Sheri's age (x) 4 years from now Dan's age (x) 10 years ago number of cents in quarters x-7 10 - x x+4 x - 10 25x number of cents in 2x dimes number of cents in x + 5 nickels Separate 17 into two parts Distance traveled in (x) hours at 50 mph 10(2x) 5(x + 5) x and 17 - x 50x Two consecutive integers two consecutive even integers two consecutive odd integers Interest in (x) dollars for 1 year at 5 percent $20,000 separated into two investments x and x+1 x and x+2 x and x+2 0.05x x and $20,000 - x Distance traveled in 3 hours at (x) mph Distance traveled in 40 minutes at x mph (40 minutes = 2/3 hour) Sum of a number and 20 product of a number and 3 3x 2x / 3 x + 20 3x quotient of a number and 8 four times as much three is four more than a number x/8 4x 3=x+4 Facts to remember 1. 2. 3. 4. 5. “Times as much” means to multiply “More than” means add. “Decreased by” means subtract “Increased by” means add “Separate 28 into two parts” means find two numbers whose sum is 28 6. “Percent of” means multiply 7. “Is, was, will be, and are” becomes the equals sign (=) in algebra. 8. If 7 exceeds 2 by 5, then 7 – 2 = 5. “Exceeds” becomes a minus sign (-), and “by” becomes an equal s sign (=).