Desmond has w marbles and Mandy has 1/2 w marbles. Desmond gives one-tenth of his marbles and Mandy gives two-fifth of her marbles to their cousin Joel. Write an expression for the number of marbles Joel receives.
? + ? = ?
Joel received ? marbles
w(1/10) + (1/2 w)(2/5) = w(1/10 + 1/5) = _____
Desmond gives one-tenth of his marbles, which is (1/10)w.
Mandy gives two-fifth of her marbles, which is (2/5)(1/2w) = (1/5)w.
The number of marbles Joel receives is the sum of what Desmond gives and what Mandy gives, so the expression for the number of marbles Joel receives is (1/10)w + (1/5)w.
Simplifying the expression, we get (1/10 + 1/5)w.
Since 1/10 + 1/5 = 1/10 + 2/10 = 3/10, the expression becomes (3/10)w.
Therefore, Joel receives (3/10)w marbles.
To find the expression for the number of marbles Joel receives, let's break down the given information step by step:
1. Desmond has "w" marbles.
2. Mandy has "1/2 w" marbles, which means she has half as many marbles as Desmond.
Desmond gives one-tenth of his marbles to Joel, which is equal to (1/10)w marbles.
Mandy gives two-fifths of her marbles, which is equal to (2/5)(1/2 w) marbles. Simplifying this expression, we get (1/5)w marbles.
Now, we can add these two expressions to find the total number of marbles that Joel receives:
(1/10)w + (1/5)w = (1/10 + 1/5)w
= (1/10 + 2/10)w
= (3/10)w
Therefore, the expression for the number of marbles Joel receives is (3/10)w.
Joel received (3/10)w marbles.