Tony and Cleo are donating some of their books to a hospital. If Tony contributes half of his books and Cleo gives one third of
hers, they will donate a total of 30 books. If tony gives two fifths of his books and Cleo contributes half of hers, they will donate a total of 31 books. How many books does each have?
Short Answer: Tony 40 Cleo 30 Givens T = Tony C = Cleo
Equations 1/2 T + 1/3 C = 30 (1) 2/5 T + 1/2 C = 31 (2)
Adjustments Multiply (1) by 3 Multiply (2) by 2
New Equations 3/2 T + C = 90 (1a) <u>4/5 T + C = 62</u> (2a) Subtract (2a) from (1a) (3/2 - 4/5)T = 28 the common multiple of 2 and 5 = 10. (15/10 - 8/10)T = 28 7/10 T = 28 Multiply by 10 7T = 28*10 7T = 280 Divide by 7 T = 280/7 = 40
Put T = 40 into (1) 1/2 T + 1/3 C = 30 1/2 (40) + 1/3 C = 30 20 + 1/3 C = 30 Subtract 20 from both sides. 1/3 C = 30 - 20 1/3 C = 10 Multiply through by 3 C = 10 * 3 C = 30
Answer: Cleo has 30 books. Tony has 40 books.
Check <em>Use Equation 2</em> 2/5 T + 1/2 C = 31 2/5*40 + 1/2 * 30 = ? 31 16 + 15 =?3` 31 = 31 They are equal.