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### Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation2.14 Word Problems - Basic Operations With Variables - Challenging

 Example: Question: A taxicab charges \$2.00 for a ride, plus \$0.40 for each mile, m, driven. The cab driven hopes to make a minimum of \$5.00 from his next customer. Write and equation that could be used to solve for the value of m? Solution: The cab driver wants to make a minimum of \$5 on his next fare. this means that he will make an amount equal to or greater than \$5. So the correct inequality should contain>=5. the cost of the cab ride is the sum of the fixed and variable costs. the fixed costs is \$2. The variable cost is \$0.40 for each of m miles driven. This makes the variable cos .40m. So the total inequality is 2 + 0.40m >= 5. Directions: Write the algebraic equation for the following word problems.
 Q 1: A bag contains a total of 27 lollipops, all of which are either lemon, grape or cherry. Twice as many lemon as grape. three fewer lollipops than lemon and cherry. Which equation can be used to solve for the number of grape lollipops in the bag? (Hint: Let x be number of grape lollipops. Twice as many pops are lemon as grape, so there are 2x lemon pops. Three fewer pops than lemon are cherry, so there are 2x-3 cherry pops. There are total 27 pops, so sum these three variable expressions to 27= ?)x + 3n + (3n-2) = 27x 2x + 3x = 27x+2x+(2x-3)=27 Q 2: Jan has read 8 pages of her social studies chapter. She wants to read a minimum of y pages before she goes to bed. If z represents the additional pages she must read, which of the following best represents the number of pages Jan must read before going to bed? z - 8 >= y8 + z >= y Q 3: A computer repair company charges \$50 for a service call plus \$25 for each hour of work. Which of the following equation represents the relationship between the bill, b, for a service call, and the number of hours spent on the call, h?50 + 25h = b50h + 25 = b50 += 25 = b Q 4: Richard has 5 fewer than three times as many games for Nintendo than he has for Play Station. If Richard has a total of 23 games, which of the following equation can be used to solve for the number of Play Station games he has? (Hint: Let x be the number of Play Station games. Richard has 5 fewer than three times as many Nintendo games as Play Station games; three times as many is 3x, so 5 fewer than this is 3x-5. Richard has total of 23 games so sum these two variable expressions to _______)x + (5x-3) = 23x + (3x-5) = 23 Q 5: Ben ate 3 more slices of pizza than Peter. George ate half as many slices of pizza as Ben. The boys ate a total of 12 slices of pizza. Which of the following equations could be used to solve for the number of slices of pizza that Peter ate.p + (p+3) + (p+3)/2 = 12p + (p+3) + 2/p = 123p = 12 Q 6: Emma and Jan went shopping. Emma spent \$10 less than twice as much as Jan. If the two girls spent a total of \$140, which of the following equations could be solved for the amount that Jan spent? x + (2x-10) = 140x + (2x-10) = 1402x - 10 = 140 Q 7: Bob is allowed to have a maximum of m treats per day. He has already had b treats today. if t is the number of treats Bob is still allowed to have, which of the following best represents this situation?b - t <= mb + t <= mbt = m Q 8: Ron is 8 years more than half as old as Reed. Their total ages sum to 50. Which of the following equations can be used to solve for Reed's age? (Hint: Let R be Reed's age. Ron is 8 years more than half as old as Reed; half as old as Reed is R/2, so 8 years more than this is R/2 +8. Their ages total 50, so sum these two variable expressions to 50: _____)R + (R+8)/2 = 50R/2 + R/6 = 50R + (R/2 + 8) = 50 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!