Answer:
[tex]d < \frac{3}{2}x[/tex]
Step-by-step explanation:
Represent a cup with x; the cat with c and the dog with d
From the first statement, we have:
[tex]c < x[/tex]
From the second, we have:
[tex]c = \frac{1}{3}d + \frac{1}{2}x[/tex]
Required
Express d in terms of x
We have:
[tex]c = \frac{1}{3}d + \frac{1}{2}x[/tex] and [tex]c < x[/tex]
Merge both expressions to give:
[tex]\frac{1}{3}d + \frac{1}{2}x < x[/tex]
Collect Like Terms
[tex]\frac{1}{3}d < x - \frac{1}{2}x[/tex]
[tex]\frac{1}{3}d < \frac{1}{2}x[/tex]
Multiply both sides by 3
[tex]3 * \frac{1}{3}d < \frac{1}{2}x * 3[/tex]
[tex]d < \frac{3}{2}x[/tex]
