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Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation2.18 Word Problems - Numbers

 Example: One whole number is three times another. Together the numbers add up to 84. Find both numbers. Let x be the first whole number. Let 3x be the second whole number. The two numbers add up to 84 : x + 3x = 84 4x = 84 x = 21 3x = 63 Therefore the first number is 21 and second number is 63. Example: One whole number is three times a second. If 20 is added to the smaller number, the result equals 6 more than the larger number. Find both numbers. let the smaller number be s and larger number be l l = 3s s + 20 = l + 6 s + 20 = 3s + 6 14 = 2s s = 7 l = 3s = 3x7 = 21 Example: Separate 45 into two parts such that twice the smaller is 9 less than the larger. Let x = the smaller part Let 45 - x = the larger part twice the smaller is 9 less than the larger: 2(x) = (45-x)- 9 2x = 45 - x - 9 3x = 36 x = 12 which is the smaller part larger part = 45 - x = 45 - 12 = 33 Directions: Answer the following questions.
 Q 1: The larger of two whole numbers is five times the smaller. If the larger number is increased by 3, it equals 15 more than the smaller. find both numbers. (Hint: let x be smaller number, 5x the larger number. If the larger number is increased by 3, it equals 15 more than smaller number: 5x + 3 = x + 15 solve for x and 5x)smaller number is 2 and larger number is 10smaller number is 3 and larger number is 15smaller number is 4 and larger number is 20 Q 2: Separate 29 into two parts such that three times the smaller is 19 more than the larger. (Hint: let x be the smaller part and 29-x the larger part. 3x = l + 19. Solve for x and 45-x) smaller number is 10 and larger number = 19smaller number is 12 and larger number = 17smaller number is 9 and larger number = 20 Q 3: Five more than three times a whole number is 71. Find the number. (Hint: 3x + 5 = 71 then x = ____)212232 Q 4: Separate 45 into two parts such that twice the smaller is 9 less than the larger. Find the numbers.32 and 1133 and 1233 and 14 Q 5: Six less than twice a number is 48. Find the number. (Hint: the algebraic equation can be written as 2x - 6 = 48 solve for x)272524 Q 6: One whole number is 12 more than another. If the two numbers add up to 70, find both numbers. (Hint: a = b + 12 , a + b = 70, a= ?, b = ?)29 and 4131 and 3930 and 40 Q 7: Separate 15 into two parts such that twice the smaller is 3 more than the larger. (Hint: Let x be the smaller part, then larger part is 15-x. Twice the smaller is three more than the larger: 1(x) = (15 - x) + 3 solve for x and then find the larger number which is 15-x)smaller number is 5 and larger number is 10smaller number is 7 and larger number is 8smaller number is 6 and larger number is 9 Q 8: The larger of two whole numbers is 7 more than the smaller. Double the smaller number equals 8 more than the larger number. Find both numbers. (Hint: let l be larger number and s be the smaller number. l = 7 + s, 2s = l+8 solve for s and l) s = 14 and l = 21s = 13 and l = 20s = 15 and l = 22 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!