Question

There are two red jars of marbles and one blue jar of marbles. Jars of a certain color have the same number of marbles in them. There are 42 marbles in total. The difference between the number of marbles in a red jar and the number of marbles in a blue jar is 12. Find the number of marbles in each type of jar.

Answer 1

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.