2.5 Problem Solving: Direct Translation Problems Involving Percent Learning Objectives: 1. Translate English phrases to algebraic expressions or to equations. 2. Solving direct translation problems. 1. Translate English phrases to algebraic expressions or to equations Key words: Sum minus times divided by is More than subtracted from product quotient of was Plus the difference of reciprocal yields Increased by decreased by multiply by ratio equals Added to less than twice results in Greater than Fewer than triple is equal to Exceed by less double is equivalent to Combine Altogether Example 1. Translate each phrase to an algebraic expression or an equation. Let x represents the unknown number. 1. 2 less than twice an unknown number 2. The sum of twice a number and 29 3. Twice the difference of a number and (−3) 4. The quotient of a number and 13, increased by 5 5. An unknown number decreased by 12 is 207 6. 48 is 29 less than twice a number 7. Twice the sum of a number and 31 is the same as 3 more than the number 2. Solving direct translation problems. Consecutive Numbers: Consecutive Numbers: Consecutive Odd/Even Numbers: 1st 2nd 3rd 4th 1 Steps for Solving Problems with Mathematical Models 1. Identify what you are looking for; read the problem very carefully. 2. Choose the variable the unknown; what is being asked” 3. Translate the problem into the language of mathematics. 4. Solve the equation(s) found in step 3. 5. Check the reasonableness of your answer. 6. Write your answer in a complete sentence. Example 2. Translate each phrase to an algebraic expression and solve. Let x represents the unknown number. 1. Twice a number is increased by 40. This result is the same as the number decreased by 7. Find the number. 2. The sum of 3 consecutive odd integers is −87. Find the middle integer. 3. The cost of a calculator is $2.50 less than five times the cost of a notebook. If Jordan purchases one calculator and one notebook, the total cost is $20. Find the cost of the calculator. 4. You need to rent a moving truck for a day. You have identified two companies that rent trucks. Company A charges $40 per day plus $0.20 per mile. Company B change $30 per day plus $0.25 per mile. For how many miles will the cost of renting be the same? 2