Question

PLEASE SHOW WORKING!!!!!!

A piece of wood is of length 45 cm. The length is divided in the ratio 7 : 2
Work out the length of each part.

Answer 1

7 : 2

35 cm : 10 cm

Explanation:

7 : 2

7 + 2 = 9

45 ÷ 9 = 5

7 : 2

7 × 5 : 2 × 5

35 : 10

Answer 2

Explanation:

Alright let's get started!

Here are TWO WAYS to get the answer!

WAY ONE:

Our Information:

1. 45 cm piece of wood divided in the ratio of 7 : 2
2. 7x and 2x are the lengths

Ok, time to work this out!

Our new equation will now be;

7x + 2x = 45

Collecting the like terms in the left side we get;

9x = 45

Divide by 9 on both sides;

x =
`(45)/(9)`

Simplify;

x = 5

Find the values for the 7 : 2 ratio by substituting x;

5 × 7 = 35 cm

5 × 2 = 10 cm

Final Results:

`(35)/(10)` =
`(7)/(2)`

↓(Pretend This is a Chart)↓

Piece 1 Piece 2

7 2

14 4

21 6

28 8

35 10 35 + 10 = 45

WAY TWO (this will be more explaining so for show your work I suggest way 1)

Since the ratio is 7 : 2, you can start by thinking of it as 9 pieces.

If you divided the board into 9 equal pieces, they'd each 5 inches long, because 45 divided by 9 = 5.

But since they're in the 7 : 2 ratio, you have (7 x 5) to (2 x 5), or 35 : 10

So one is 35 inches, the other is 10.

In simpler words, it's 7x + 2x = 45. (So 9x = 45, and x = 5. So 7x = 35, and

2x = 10.)

YAY!!! WE SURVIVED!!!