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?
connie = c
danny = d = .6 c
owen = o = 1.2 d = 1.2*.6 c = .72 c
o = c - 21
so
o = c-21 = .72 c
.28 c = 21
c = 75
d = .6 c = 45 the end
Let's assume that Danny has x marbles.
According to the given information, Owen has 20% more marbles than Danny. This means Owen has 1.2x marbles.
Danny has 40% less marbles than Connie. So, Connie has 1 + 0.4 = 1.4x marbles.
Owen has 21 marbles less than Connie. This means 1.2x = 1.4x - 21.
Simplifying the equation, we get:
0.2x = 21.
Dividing both sides by 0.2, we get:
x = 21 / 0.2 = 105.
Therefore, Danny has 105 marbles.
To determine how many marbles Danny has, we need to go step by step.
Let's start by assuming Danny has 'x' number of marbles.
Since Owen has 20% more marbles than Danny, Owen must have (x + 20%x) = (x + 0.2x) = 1.2x marbles.
Now let's move on to the next piece of information. It says that Danny has 40% less marbles than Connie. So, if Danny has 'x' marbles, Connie must have (x + 40%x) = (x + 0.4x) = 1.4x marbles.
Finally, it states that Owen has 21 marbles less than Connie. Therefore, we can set up an equation:
1.2x = 1.4x - 21
To solve for 'x', we need to bring the variables to one side of the equation:
1.4x - 1.2x = 21
0.2x = 21
To isolate 'x', we divide both sides of the equation by 0.2:
x = 21 ÷ 0.2
x = 105
So, Danny has 105 marbles.