Math Snap

STEP 1

1. Let the number of sweets I ate be represented by $x$.
2. For every one sweet I eat, you eat three sweets.
3. The total number of sweets we both ate is 32.

STEP 2

1. Set up the relationship between the number of sweets I ate and the number of sweets you ate.
2. Form an equation representing the total number of sweets eaten based on the given relationship.
3. Solve the equation to find the number of sweets I ate.

STEP 3

Let $x$ be the number of sweets I ate. According to the problem, for every one sweet I eat, you eat three sweets. Therefore, you ate $3x$ sweets.

STEP 4

The total number of sweets we both ate can be written as the sum of the sweets I ate and the sweets you ate. Hence, the equation is:
$$x + 3x = 32$$

STEP 5

Combine like terms to simplify the equation:
$$4x = 32$$

STEP 6

Solve for $x$ by dividing both sides of the equation by 4:
$$x = \frac{32}{4}$$

Simplify the right-hand side to find the value of $x$:
$$x = 8$$ Solution:
I ate $8$ sweets.