Word Problems Numerical Solutions Thursday, April 04, 2019Thursday, April 04, 2019

Two pages are back-to back in a book Two pages are back-to back in a book. If the sum of the page numbers is 203, what is the larger page number? 1 Smaller page number = x Larger page number = x + 1 Smaller Larger + = Sum of pages x + x + 1 = 203 Answer Larger = x + 1 = 101 + 1 = 102 2x + 1 = 203 –1 –1 2x = 202 x = 101

x – 2 3(x – 2) 3(x – 2) = x + 6 2x – 6 = 6 3x – 6 = x + 6 +6 +6 –x –x If 2 is subtracted from a number and this difference is tripled, the result is 6 more than the number. Find the number. 2 Let number = x ‘2 is subtracted from a number’ = x – 2 3(x – 2) ‘The difference is tripled’ = 3(x – 2) = x + 6 2x – 6 = 6 3x – 6 = x + 6 +6 +6 –x –x 2x = 12 2x – 6 = 6 x = 6

Larry books Judy books x 2x – 3 5 2(5) – 3 10 – 3 7 Judy has 3 less than twice the number of books that Larry has. If Larry has 5 books, how many books does Judy have? 3 Larry books Judy books x 2x – 3 5 2(5) – 3 10 – 3 7

‘number is increased by 8’ = k + 8 ‘The result is doubled’ = 2(k + 8) A certain number k is increased by 8, and the result is then doubled. The new result is 8 less than 3 times the original number, k. What is the value of k ? 4 Let number = k ‘number is increased by 8’ = k + 8 ‘The result is doubled’ = 2(k + 8) 2(k + 8) = 3k – 8 16 = k – 8 2k + 16 = 3k – 8 +8 +8 –2k –2k 24 = k 16 = k – 8

Let 1st integer = x 19 Let 2nd integer = x + 1 19+1 = 20 If the sum of three consecutive integers equals 60, what is the greatest of the integers? 5 Method #1 Let 1st integer = x 19 Let 2nd integer = x + 1 19+1 = 20 Let 3rd integer = x + 2 19+2 = 21 x + x + 1 + x + 2 = 60 3x + 3 = 60 –3 –3 3x = 57 x = 19

If the sum of three consecutive integers equals 60, what is the greatest of the integers? 5 Method #2 Test each answer, assuming it is the greatest integer. Greatest Middle Smallest Sum A. 18 B. 19 C. 20 D. 21 E. 22 18 17 16 51 NO 19 18 17 54 NO 20 19 18 57 NO 21 20 19 60 YES

Let 1st integer = x 13 Let 2nd integer = x + 2 13+2 = 15 If the sum of two consecutive odd integers is 28, what is the product? 6 Let 1st integer = x 13 Let 2nd integer = x + 2 13+2 = 15 x + x + 2 = 28 Sum = 13 + 15 = 28 2x + 2 = 28 –2 –2 2x = 26 Product = 13  15 = 195 x = 13

Let number = x x2 – x = 4x + 6 –4x – 6 –4x – 6 x2 – 5x – 6 = 0 If half the difference between the square of a certain positive number and the number is 3 more than twice the number, what is the number? 7 Let number = x x2 – x = 4x + 6 –4x – 6 –4x – 6 x2 – 5x – 6 = 0 (x – 6)(x + 1) = 0 x – 6 = 0 x + 1 = 0 1(x2 – x) = 2(2x + 3) x = 6 x = –1

Cost of pencil = A Cost of pen = B Jon  1A + 2B = 3.50 Lauren  Jon buys one pencil and two pens for $3.50. Lauren buys four pencils and three pens for $5.50. How much would one pencil and one pen cost? 8 Cost of pencil = A Cost of pen = B Jon  1A + 2B = 3.50 (Multiply Jon by –4) Lauren  4A + 3B = 5.50 Jon  –4A – 8B = –14.00 Add Equations Lauren  4A + 3B = 5.50 – 5B = –8.50 B = 1.70 (Pen cost)

the original equations. 1A + 2B = 3.50 1A + 2B = 3.50 4A + 3B = 5.50 Jon buys one pencil and two pens for $3.50. Lauren buys four pencils and three pens for $5.50. How much would one pencil and one pen cost? 8 Cost of pencil = A Cost of pen = B B = 1.70 (Pen cost) Find A. Use one of the original equations. 1A + 2B = 3.50 1A + 2B = 3.50 4A + 3B = 5.50 A + 2(1.70) = 3.50 Cost of pencil and pen = A + B = 0.10 + 1.70 = 1.80 A + 3.40 = 3.50 A = 0.10