ken spend 1/5 of his money on a dictionary. he gives $21 to his brother and has 1/2 of his money left. how much money does ken have left?

if he starts out with x, we have

(x - x/5) - 21 = x/2
x = 70

check:
1/5 of 70 is 14

70-14-21 = 35, which is 1/2 of 70

To find out how much money Ken has left, we need to follow these steps:

Step 1: Let's assign a variable to unknown. Let's say x is Ken's original amount of money.

Step 2: Ken spends 1/5 of his money on a dictionary. So, he spends (1/5) * x = x/5 on the dictionary.

Step 3: After spending on the dictionary, Ken has (x - x/5) amount of money remaining, which is equivalent to (4/5) * x.

Step 4: Ken gives $21 to his brother, so the remaining money after giving $21 would be [(4/5) * x] - $21.

Step 5: According to the question, Ken has 1/2 of his money left. So, we can set up the equation:
[(4/5) * x] - $21 = (1/2) * x.

Now, let's solve the equation to find the value of x, which represents Ken's original amount of money.

[(4/5) * x] - $21 = (1/2) * x

Multiply both sides of the equation by 10 to eliminate the fractions:
8x - 210 = 5x

Subtract 5x from both sides:
3x - 210 = 0

Add 210 to both sides:
3x = 210

Divide both sides by 3:
x = 70

So, Ken's original amount of money was $70.

Finally, to find out how much money Ken has left after giving $21 to his brother, we substitute x = 70 into the equation [(4/5) * x] - $21:

[(4/5) * 70] - $21 = (56/5) - $21 ≈ $44.8 - $21 = $23.8.

Therefore, Ken has approximately $23.8 left after giving $21 to his brother.