Answer:
h.56
Step-by-step explanation:
 
        
                    
             
        
        
        
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.
        
             
        
        
        
The answer will be 53/135, or in decimal form, 0.39259259...
        
             
        
        
        
If sinα=cosß  it means that ß=90-α.  This also means that α+ß=90 so we can say:
4k-22+6k-13=90
10k-35=90
10k=125
k=12.5°
...
The above identity comes up a lot, and is one worth committing to memory for sure. 
sinα=cos(90-α) or vice versa cosα=sin(90-α)