Robert gave one-half of his marbles to Dean. Then he gave two-thirds of the remaining ones to Mark. If he ended up with 10, how many did he have when he stsrted?
The 10 marbles he had left would be the same as one-third, so multiply by 3 to get how many marbles he had after he gave half of them to Robert. 10x3=30. Since 30 is half of what he orginally had, multiply by 2. 2x30=60. He started with 60 marbles.
To find the number of marbles Robert had when he started, we need to work backwards from the given information.
Let's denote the number of marbles Robert had when he started as "x".
First, Robert gave one-half of his marbles to Dean. This means he had x/2 marbles left.
Next, he gave two-thirds of the remaining ones (x/2) to Mark. This means he gave (2/3) * (x/2) = x/3 marbles to Mark.
After this second gift, Robert ended up with 10 marbles.
Setting up an equation to represent the given information, we have:
x - (x/2) - (x/3) = 10
To solve this equation, we can simplify the left side by finding a common denominator:
(6x - 3x - 2x) / 6 = 10
Simplifying further, we have:
(x/6) = 10
To isolate x, we can multiply both sides of the equation by 6:
x = 10 * 6
Therefore, Robert had x = 60 marbles when he started.