Jack was given an end-of-year bonus. First, he gave half of his bonus to his parents and $40 to his niece. Next, he donated 2/3 of the remaining bonus to a charity. Finally, he spent 1/3 of his remaining bonus on some clothes and $10 on a bag. If he had $110 left, how much was his bonus?
I think it 161 if you add 110+40+10+2/3+1/3=161 but I don't think that's how you do it
starting with x, we have
niece: 40
charity: 2/3 (x-40)
clothes: 1/9 (x-40)
bag: 10
left over: 110
so, now you have
40 + 2/3 (x-40) + 1/9 (x-40) + 10 + 110 = x
x = 580
To find out how much Jack's bonus was, let's work through the problem step by step.
1. Jack gave half of his bonus to his parents and $40 to his niece. This means he's left with half of his bonus minus $40.
Let's call this remaining amount X.
X = (1/2) * Bonus - $40
2. Next, he donated 2/3 of the remaining bonus to a charity. This means he's left with two-thirds of X.
Let's call this remaining amount Y.
Y = (2/3) * X
3. Finally, he spent 1/3 of his remaining bonus on some clothes and $10 on a bag. This leaves him with $110.
Let's call this remaining amount Z.
Z = (1/3) * Y - $10 = $110
Now, we can solve for Z to find Jack's bonus.
(1/3) * Y - $10 = $110
(1/3) * [(2/3) * X] - $10 = $110
(2/9) * X - $10 = $110
By isolating X, we have:
(2/9) * X = $110 + $10
(2/9) * X = $120
Now, let's solve for X:
X = ($120 * 9) / 2
X = $1080 / 2
X = $540
Therefore, Jack's bonus was $540.