Answer:
Explanation:
Let's use variables to represent the number of marbles in each jar.
Let r be the number of marbles in a red jar and b be the number of marbles in a blue jar. Since the jars of a certain color have the same number of marbles, we know that there are 2 red jars with r marbles each, and 1 blue jar with b marbles.
We know that the total number of marbles is 42, so we can write an equation:
2r + b = 42
We also know that the difference between the number of marbles in a red jar and the number of marbles in a blue jar is 12, so we can write another equation:
r - b = 12
Now we have two equations with two variables. We can solve for r and b using substitution or elimination.
Let's solve for b in the second equation:
r - b = 12
b = r - 12
Substituting this expression for b into the first equation:
2r + b = 42
2r + (r - 12) = 42
3r - 12 = 42
3r = 54
r = 18
So each red jar has 18 marbles. Substituting this value of r into the equation for b:
b = r - 12
b = 18 - 12
b = 6
So the blue jar has 6 marbles.
Therefore, there are two red jars with 18 marbles each, and one blue jar with 6 marbles.