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 weight of the blue marble?

Answer 1

The weight of a blue marble is found by solving a system of linear equations representing the total weight of combinations of red and blue marbles. By using elimination, we determine that the weight of a blue marble is 18 grams.

Step-by-step explanation:

The question involves determining the weight of a blue marble based on a system of linear equations. We have two equations based on the information provided:

1. 4R + 7B = 190
2. 12R + 5B = 282

where R represents the weight of a red marble and B represents the weight of a blue marble. To find the weight of a blue marble, we can use the method of substitution or elimination to solve for B. Here is a step-by-step breakdown using elimination:

1. Multiply the first equation by 3 to align the coefficient of R with the second equation: (3×4)R + (3×7)B = 3×190 which simplifies to 12R + 21B = 570.
2. Subtract the second equation from this new equation: (12R + 21B) - (12R + 5B) = 570 - 282 which gives us 16B = 288.
3. Divide both sides by 16 to find the weight of a blue marble: B = 288 / 16, which equals 18 grams.

So, the weight of the blue marble is 18 grams.