Problem 554 - Prealgebra

Question

Cooking Ratika is making rice for a dinner party. The number of cups of water is twice the number of cups of rice. If Ratika plans to use 4 cups of rice, how many cups of water does she need?

Step-by-Step Solution

Answer

8 cups.

Step 1: Understand the Problem

Ratika needs twice as many cups of water as she uses cups of rice. She plans to use 4 cups of rice.

Step 2: Set Up the Equation

Let the number of cups of rice be represented by \( r \) and the number of cups of water be represented by \( w \). According to the problem, \( w = 2r \).

Step 3: Substitute the Known Value

Ratika plans to use 4 cups of rice, thus \( r = 4 \). Substitute this value into the equation: \( w = 2 \times 4 \).

Step 4: Calculate the Cups of Water

Perform the multiplication to find the number of cups of water: \( w = 8 \). Ratika needs 8 cups of water.

Key Concepts

solving equations

Solving equations involves finding the value of an unknown variable that makes the equation true. When Ratika is making rice, we use the equation to represent the relationship between the cups of water and rice. The equation is set up as follows: Let:

• the number of cups of rice be represented by \( r \)
• the number of cups of water be represented by \( w \).

According to the problem, the relationship is \( w = 2r \). This means there are twice as many cups of water as cups of rice. To understand this equation, think of \( r \) as a known value, in our case, 4 cups of rice. By substituting the value of \( r \) in the equation, we can solve for \( w \): \( w = 2 \times 4 \). This straightforward approach allows us to calculate the exact number of cups of water needed.

multiplication

Multiplication is a mathematical process used to find the total number of items when groups of equal size are combined. In the rice example, we use multiplication to find out how much water Ratika needs. Here’s the multiplication we perform:

• We know the relationship between rice and water is given by \( w = 2r \), where each cup of rice needs twice as many cups of water.
• Since Ratika plans to use 4 cups of rice, we replace \( r \) with 4.

Using the equation: \( w = 2 \times 4 \) Calculating it: \( w = 8 \) So, Ratika needs 8 cups of water. This simple multiplication helps us quickly solve such proportional relationships. Multiplication is a fundamental operation in math that you will use often in various problems.

problem-solving steps

Solving a math problem successfully involves breaking it down into clear and manageable steps. Here’s a breakdown of the steps used in this exercise: Step 1: Understand the Problem

• Identify what you know: Ratika needs twice as many cups of water as rice.
• Identify what you need to find: The number of cups of water for 4 cups of rice.

Step 2: Set Up the Equation

• Represent the cups of rice as \( r \) and the cups of water as \( w \).
• Formulate the relationship: \( w = 2r \).

Step 3: Substitute the Known Value

• Ratika plans to use 4 cups of rice, so \( r = 4 \).
• Substitute this value into the equation: \( w = 2 \times 4 \).

Step 4: Calculate the Cups of Water

• Perform the multiplication to get \( w = 8 \).
• Ratika needs 8 cups of water.

Following these steps helps ensure you understand and solve the problem correctly. Breaking down each step is key to becoming proficient in problem-solving.