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)

4/5 T + C = 62 (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

Use Equation 2

2/5 T + 1/2 C = 31

2/5*40 + 1/2 * 30 = ? 31

16 + 15 = ?3'

31 = 31 They are equal.