Question

A box contains 210 marbles which are either red or blue. There are 12 more red marbles than blue marbles. How many red marbles are in the box?

Answer 1

There are 111 red marbles in the box, calculated by setting up a system of equations using x to represent the number of blue marbles and solving for x + 12 to find the number of red marbles.

Step-by-step explanation:

To solve the problem, we can set up a system of equations. Let x represent the number of blue marbles, and x + 12 represent the number of red marbles, since the problem states there are 12 more red than blue marbles.

The total number of marbles is given as 210, so we can write the equation:

x + (x + 12) = 210

Simplifying that, we get:

2x + 12 = 210

2x = 198

x = 99

So, there are 99 blue marbles. Since there are 12 more red marbles than blue, we calculate the number of red marbles as:

x + 12 = 99 + 12 = 111

Thus, there are 111 red marbles in the box.

Answer 2

Let x and y be the number of red and blue marbles, respectively.

Since there are 12 more red marbles than blue ones, we have an equation:
x- y= 12 (1)

On the other hand, we also know that:
x+ y= 210 (2)

x- y= 12 (1)
x+ y= 210 (2)

Take (1)+ (2), we have:
(x- y)+ (x+ y)= 12+ 210
⇒ 2x= 222
⇒ x= 222/2
⇒ x= 111

There are 111 red marbles.

Hope this helps.