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MTH 091 Sections 3.4 and 9.4 Linear Equations in One Variable and Problem Solving Six Problem Solving Steps 1. 2. 3. 4. 5. 6. Read the problem. Assign a variable. Write an equation. Solve the equation. State the answer. Check the answer. Examples 1. Three times a number, added to 9, is 33. Find the number. 2. The difference of a number and five is equal to the quotient of 36 and 4. Find the number. 3. A popular tablet and an accessory kit are sold for $560. The cost of the tablet is three times as much as the cost of the accessory kit. Find the cost of the tablet and the cost of the accessory kit. More Examples 4. Twenty subtracted from six times a number is five more than the number. Find the number. 5. The sum of twice a number and seven is equal to the sum of the number and nine. What is the number? 6. A 48 inch board is to be cut into three pieces so that the second piece is four times as long as the first piece and the third piece is seven times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces. Still More Examples 7. 8. 9. The sum of two consecutive page numbers of an open book is 359. Find the page numbers. When eight is added to a number, and then the sum is multiplied by five, the result is -40. What is the number? A car rental company charges a daily rate of $35 plus $0.50 per mile. Suppose that you rent the car for a day, and your bill is $120. How many miles did you drive? Just A Few More Examples 10. Twice the difference of a number and six is equal to three times the sum of the number and five. Find the number. 11. A number subtracted from -35 amounts to 182. What is the number?