Question

A bag contains yellow marbles and red marbles, 23 in total. The number of yellow marbles is 4 less than 2 times the number of red marbles. How many yellow marbles are there?

Answer 1

First let’s express the total number of marbles as such:
y(yellow marbles) + r(red marbles)=23; y+r=23

now let’s express the relation of yellow marbles to red marbles:
y=2r(2 times red marbles) - 4(4 less marbles); y=2r-4

since we figured out what y equals, we can plug into the first equation we created:
(2r-4)+r=23

now solve for r:
2r-4+r=23
combine like terms
3r-4=23
add 4 to both sides
3r=27
divide both side by 3
r=9

plug r back into first equation and solve for y:
y+9=23
subtract 9
y=14

there are 9 red marbles and 14 yellow marbles!