Questions: Filbert the cat eats twice the amount of food as another cat, Kiko. If together they eat three-quarters of one cup of cat food at each meal, which of the following equations will give you the number of cups, x, that Kiko eats at each meal? a.) 3x = 3/4 b.) 2x = 3/4 c.) 3/4 x = 2 d.) 3/4 x = 3

Solution Steps

To solve this problem, we need to set up an equation based on the given information. Let \( x \) be the amount of food Kiko eats. Since Filbert eats twice as much as Kiko, Filbert eats \( 2x \). Together, they eat \( x + 2x = 3x \) cups of food. We know that together they eat three-quarters of a cup, so we set up the equation \( 3x = \frac{3}{4} \).

Let \( x \) be the amount of food Kiko eats at each meal. Since Filbert eats twice as much as Kiko, Filbert eats \( 2x \).

Together, Kiko and Filbert eat \( x + 2x = 3x \) cups of food at each meal. We know that together they eat \(\frac{3}{4}\) of a cup of food. Therefore, we set up the equation: \[ 3x = \frac{3}{4} \]

To find \( x \), we solve the equation: \[ 3x = \frac{3}{4} \] Dividing both sides by 3, we get: \[ x = \frac{3}{4} \div 3 = \frac{3}{4} \times \frac{1}{3} = \frac{3}{12} = \frac{1}{4} \] Thus, \( x = 0.2500 \).

Final Answer