Owen has 20% more marbles than Danny. Danny has 40% less marbles than Connie. Owen has 21 marbles less than Connie. How many marbles does Danny have?

o = 1.2d

d = 0.6c
o = c-21

c-21 = 1.2(0.6c)
c = 75

d = .6c = 45

Please explain O = 1.2d

Steve, could you please explain how you got c = 75

The o,c,d stand for Owen, Danny, Connie.

We are told that Owen has 20% more than Danny, so o=1.2d (d + .2*d)

Now, just start substituting...

o = 1.2d
o = c-21
So,

c-21 = 1.2d

But, we also know that d = 0.6c, so

c-21 = 1.2(0.6c)
c-21 = .72c
.28c = 21
c = 75

actually, we don't really need to know what c is. We could have substituted the other way, but the arithmetic gets a bit messier:

c-21 = 1.2d
(d/.6)-21 = 1.2d
d(1/.6 - 1.2) = 21
d(1-.72)/.6 = 21
.28d = 12.6
d = 45

To find out how many marbles Danny has, we need to analyze the information given and solve the question step by step.

Let's assume that Danny has x number of marbles.

According to the first statement, Owen has 20% more marbles than Danny. This means Owen has 120% (100% + 20%) of x marbles, which can be written as 1.2x marbles.

The second statement says Danny has 40% less marbles than Connie. This means Danny has 60% (100% - 40%) of Connie's marbles. Therefore, we can write it as 0.6c, where c represents the number of marbles Connie has.

Lastly, the third statement states that Owen has 21 fewer marbles than Connie. So, we can write it as c - 21.

According to the given information, we can set up the following equation:
1.2x = 0.6c - 21

Now, we need to use the third statement, which tells us that Owen has 21 marbles less than Connie, to further simplify the equation:
1.2x = 0.6(c - 21) - 21

Simplifying the equation:
1.2x = 0.6c - 12.6 - 21
1.2x = 0.6c - 33.6

Since we are looking for the number of marbles Danny has (x), we can substitute (c - 21) for c in the equation:
1.2x = 0.6(c - 21) - 33.6

Now, let's solve the equation to find the value of x (the number of marbles Danny has):
1.2x = 0.6(c - 21) - 33.6
1.2x = 0.6c - 12.6 - 33.6
1.2x = 0.6c - 46.2
1.2x - 0.6c = -46.2

Now, we'll substitute the value of c (in terms of x) into the equation. From the second statement, we know that c is 40% more than x:
c = 1.4x

Substituting c = 1.4x into the equation:
1.2x - 0.6(1.4x) = -46.2
1.2x - 0.84x = -46.2
0.36x = -46.2
x = -46.2 / 0.36
x ≈ -128.33

Since the number of marbles cannot be negative, it seems there is an error or inconsistency in the information given. Please double-check the information or provide additional details to correctly solve the problem.