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Will likes two brands of healthy breakfast cereal. In Superfiber cereal, there are 5 grams of fiber in one cup. In Fiber Oats cereal, there are 4 grams of fiber in one cup. Let [tex]\( x \)[/tex] represent the number of cups of Superfiber Will ate this week and let [tex]\( y \)[/tex] represent the number of cups of Fiber Oats he ate this week.

Which inequality represents the situation if the cereal Will ate this week contained at least 30 grams of fiber?

A. [tex]\( 5x + 4y \geq 30 \)[/tex]
B. [tex]\( 5x + 4y \leq 30 \)[/tex]
C. [tex]\( 4x + 5y \geq 30 \)[/tex]
D. [tex]\( 4x + 5y \leq 30 \)[/tex]



Answer :

GinnyAnswer
To determine the correct inequality that represents the situation with Will's cereal consumption, let's analyze the problem step-by-step:

1. Identify the Variables:
- Let [tex]\( x \)[/tex] represent the number of cups of Superfiber cereal Will ate this week.
- Let [tex]\( y \)[/tex] represent the number of cups of Fiber Oats cereal Will ate this week.

2. Determine the Amount of Fiber in Each Cereal:
- Superfiber cereal contains 5 grams of fiber per cup.
- Fiber Oats cereal contains 4 grams of fiber per cup.

3. Formulate the Total Fiber Consumed:
- The fiber from the Superfiber cereal is [tex]\( 5x \)[/tex] grams.
- The fiber from the Fiber Oats cereal is [tex]\( 4y \)[/tex] grams.
- Therefore, the total fiber consumed is [tex]\( 5x + 4y \)[/tex] grams.

4. Express the Condition with an Inequality:
- Will's fiber intake from the cereals this week must be at least 30 grams.
- This gives us the inequality: [tex]\( 5x + 4y \geq 30 \)[/tex].

Hence, the inequality that represents the situation if the cereal Will ate this week contained at least 30 grams of fiber is:
[tex]\[ 5x + 4y \geq 30 \][/tex]

So, the correct answer is:

[tex]\[ 5x + 4y \geq 30 \][/tex]

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