Question

Maria's cat eats less than 1 cup of food each day. Her cat eats one-third of what Maria's dog eats plus half of a cup. What simplified inequality shows the possible amounts that Maria's dog eats in cups?

Answer 1

Answer:

$d < \frac{3}{2}x$

Step-by-step explanation:

Represent a cup with x; the cat with c and the dog with d

From the first statement, we have:

$c < x$

From the second, we have:

$c = \frac{1}{3}d + \frac{1}{2}x$

Required

Express d in terms of x

We have:

$c = \frac{1}{3}d + \frac{1}{2}x$ and $c < x$

Merge both expressions to give:

$\frac{1}{3}d + \frac{1}{2}x < x$

Collect Like Terms

$\frac{1}{3}d < x - \frac{1}{2}x$

$\frac{1}{3}d < \frac{1}{2}x$

Multiply both sides by 3

$3 * \frac{1}{3}d < \frac{1}{2}x * 3$

$d < \frac{3}{2}x$