Question

read the word problem below.

antonio has a total of 55 marbles. he has 15 green marbles and 12 red marbles. the rest of the marbles are blue. how many blue marbles does he have?

a student represents the number of blue marbles as the variable \\(b\\) and solves this problem by writing an equation. which strategy could help check the students answer?

check that the sum of \\(b\\), 12, and 15 is 55.
check that the difference of 55 and \\(b\\) is 12.
check that the sum of the \\(b\\), 27, and 15 is 55.
check that the difference of 55 and \\(b\\) is 15.

Explanation:

Define the relationship between the marble counts

$$ \text{Total Marbles} = \text{Green Marbles} + \text{Red Marbles} + \text{Blue Marbles} $$

Substitute the given values and variable

$$ 55 = 15 + 12 + b $$

Simplify the equation to find the checking strategy

$$ b + 12 + 15 = 55 $$

Answer:

• Check that the sum of b, 12, and 15 is 55. (Correct answer)
• Check that the difference of 55 and b is 12.
• Check that the sum of the b, 27, and 15 is 55.
• Check that the difference of 55 and b is 15.