Joe's marbles

1/5 × (5w + 10)

= 1/5 × 5w + 1/5 × 10
= w + 2

Or

(5w + 10) ÷ 5
= 5w ÷ 5 + 10 ÷ 5
= w + 2

Note that the term w is understood to be one time of w so there's no need to write 1 in front.


Total marbles the three of them have

= 3w + 12 + w + 2 + 5w + 10
= 3w + w + 5w + 12 + 2 + 10
= 9w + 24


Divided equally,

(9w + 24) ÷ 3

= 9w ÷ 3 + 24 ÷ 3
= 3w + 8

Area of the triangle = ½ × b × h

90cm² = ½ × b × h

Now, we can see that the triangle's height is the same as the Length of the rectangle (let's call it L)

It is given that the base is 3/5 of the Breadth of the rectangle (let's call it B)

So, we can rewrite the equation like this :

90cm² = ½ × b × h
90cm² = ½ × 3/5 × B × L

(Note that 3/5 of B is the same as saying 3/5 × B)

90cm² = 3/10 × area of rectangle

(Since area of rectangle = B × L)

We can just think of it as the area of rectangle is 10 units and area of triangle is 3 units.


So, the area of rectangle is simply:

90cm² ÷ 3 = 30cm²
30cm² × 10 = 300cm²

Alternatively,

Since 90cm² = ½ × b × h,

b × h = 90cm² × 2
b × h = 180cm²

Since b is 3/5 of B, and h = L,

to find area of rectangle we just need to do:

180cm² ÷ 3 = 60cm²
60 × 5 = 300cm²

tysm