Question

Adam buys a red marble and a blue marble. If the total weight of 4 such red marbles and 7 such blue marbles is 190g, and the total weight of 12 such red marbles and 5 such blue marbles is 282g, what is the weight of the blue marble?

A. 18g
B. 25g
C. 31g
D. 35g

Answer 1

The weight of the blue marble is calculated by setting up a system of linear equations based on the information provided about the total weights of red and blue marbles. After solving the equations, we find that the blue marble weighs 18g.

Step-by-step explanation:

To determine the weight of the blue marble, we need to set up a system of linear equations using the given information. Let's denote the weight of the red marble as r and the weight of the blue marble as b. We can use the two scenarios provided to form the following equations:

• 4r + 7b = 190g (from the first scenario)
• 12r + 5b = 282g (from the second scenario)

Now, let's multiply the first equation by 3 to align the coefficient of r with the second equation:

• 3(4r + 7b) = 3(190g)
• 12r + 21b = 570g

Next, we'll subtract the second equation from the modified first equation:

• (12r + 21b) - (12r + 5b) = 570g - 282g
• 16b = 288g

Divide both sides by 16 to get b:

• b = 288g / 16
• b = 18g

Therefore, the weight of the blue marble is 18g, which corresponds to option A.