Question

Where will her cut be located? Round to the nearest tenth. x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 A number line goes from 0 to 60. A line is drawn from 2 to 60. Genevieve is cutting a 60-inch piece of ribbon into a ratio of 2:3. Since 2 inches are frayed at one end of the ribbon, she will need to start 2 inches in. This is indicated as 2 on the number line

25.2 in.

29.4 in.

35.1 in.

40.7 in.

Answer 1

Yes i confirm the answer above is correct. A.) 25.2

Explanation:

I took the test duhh

Answer 2

The correct answer is 25.2 in.

Explanation:

It is given that number line goes from 0 to 60 which can be used to represent a ribbon of length = 60 inches.

2 inches of the ribbon are frayed so actual length = 58 inches

Please refer to the attached image for the ribbon.

A is at 0

C is at 60

B is at 2

P is the point to divide the remaining ribbon in the ratio 2:3.

Part AB of the ribbon is frayed.

BP: PC = 2:3

Let BP = 2
`x` and PC = 3
`x`

Now, BP + PC = BC = 58 = 2
`x` + 3
`x` = 5
`x`

So,

`5x =58\\\Rightarrow x =11.6`

BP =
`2* x = 2 * 11.6 = 23.2\ inches`

Location of the Cut = 2 + 23.2 = 25.2 inches

Alternatively, we can use the formula directly:

`x = \frac{m} {m + n } (x_2 - x_1) + x_1`

`x_1 = 2\\x_2 = 60`

m: n is the ratio 2:3

`x = \frac{2} {2 +3 } (60- 2) + 2\\\Rightarrow 0.4 (58 )+2\\\Rightarrow 23.2+2 \\\Rightarrow \bold{25.2\ inches}`