Answer:
[tex]Cindy = 30[/tex]
[tex]Hao= 10[/tex]
[tex]Raymond = 5[/tex]
Step-by-step explanation:
Given
Represent each withe first letter of their name;
So:
[tex]C = 3H[/tex]
[tex]R = \frac{1}{2}H[/tex]
[tex]\frac{C + R + H}{3} = 15[/tex] --- the average of books
Required
The number of book each has
Substitute [tex]C = 3H[/tex], [tex]R = \frac{1}{2}H[/tex] in [tex]\frac{C + R + H}{3} = 15[/tex]
[tex]\frac{3H + \frac{1}{2}H + H}{3} = 15[/tex]
Multiply both sides by 3
[tex]3 * \frac{3H + \frac{1}{2}H + H}{3} = 15 * 3[/tex]
[tex]3H + \frac{1}{2}H + H = 45[/tex]
Take LCM and solve
[tex]\frac{6H + H + 2H}{2}= 45[/tex]
[tex]\frac{9H}{2}= 45[/tex]
Multiply both sides by 2/9
[tex]\frac{2}{9} * \frac{9H}{2}= 45 * \frac{2}{9}[/tex]
[tex]H= 45 * \frac{2}{9}[/tex]
[tex]H= 5 * 2[/tex]
[tex]H= 10[/tex]
[tex]C = 3H[/tex]
[tex]C = 3 * 10[/tex]
[tex]C = 30[/tex]
[tex]R = \frac{1}{2}H[/tex]
[tex]R = \frac{1}{2} * 10[/tex]
[tex]R = 5[/tex]
