mr.lim gave 3600 to his wife an two children altogether. his wife received 500 more than his son. his son received twice as much as his daughter. how much did mr. lim’s wife receive?

The correct answer is: $1740$

Explanation

Let the daughter’s share be $d$, the son’s share be $s$, and the wife’s share be $w$. We are given $s = 2d$, $w = s + 500$, and $w + s + d = 3600$.

Steps:

1. Write the total with the given relations:

$$ (s+500) + s + d = 3600 $$

1. Substitute $d = \frac{s}{2}$ (since $s = 2d$):

$$ (s+500) + s + \frac{s}{2} = 3600 $$

1. Combine terms:

$$ \frac{5}{2}s + 500 = 3600 $$

1. Solve for $s$:

$$ \frac{5}{2}s = 3100 \quad\Rightarrow\quad s = \frac{3100 \times 2}{5} = 1240 $$

1. Find the wife’s amount:

$$ w = s + 500 = 1240 + 500 = 1740 $$

Therefore, Mr. Lim’s wife received $1740$.