A bag contains yellow marbles and red marbles, 16 in total. The number of yellow marbles is 1 more than 2 times the number of red marbles. How many yellow marbles are there?

Answer 1

Let Y = number of yellow marbles

R = number of red marbles

"16 in total" means:

Y + R = 16

"number of yellow marbles is 1 more than 2 times the number of red marbles" means:

Y = 1 + 2R

Now, you have a very important choice:

a) you may solve for Y

or

b) you may solve for R and then remember to solve for Y (asked by the problem)

Let's substitute for R and solve for Y directly.

R = 16 - Y [from first equation]

Y = 1 + 2(16-Y) [from second equation]

Y = 1 + 32 - 2Y

3Y = 33

Y = 11

There are 11 Yellow marbles.

Check::

From Y+R = 16, there are 5 Red marbles

Is 11 = 1 + 2(5) ?

11 = 11 ?yes

Answer 2

Y = yellow marbles

R = red marbles

Y = 2R + 1 -----> since there is 1 more than twice the red marbles

total marbles are 16

Y + R = 16

therefore

2R + 1 + R = 16

solving for R

R = 5

Thus Y = 2R + 1

Y = 11 marbles