a piece of rope 60 feet long was cut into twp pieces with lengths that were in the ratio 4:1?

Divide the length by the amount of pieces. The ratio is 4:1 (5 pieces)

60/5 = 12.

The shortest length for a 12 foot rope at a ratio of 2:1 (3 pieces) is

12/3 = 4 feet.

I'll explain why this is so:

So you have 60 ft and want a ratio of 4:1. A ratio of 4:1 makes five pieces (4 +1 = 5, get it?).

Since that means five pieces, you must divide your overall length by 5.

60/5 = 12.

Now, you want a ratio of 4:1 (which could also be written as 4/1)

So as a fractional ratio, you may multiply the top and bottom by your singular piece lengths (12 ft).

That makes 4/1 * 12/12

Multiply straight across which would be (4*12)/(1*12), giving you 48/12

Once you have the ratio of 48/12 (48:12) you have the shortest length at 12.

You repeat the previous steps once again, except using 12 ft, instead of 60.

2:1 is equal to 3 pieces.

12/3 = 4.

So the ratio of 2:1 of 12 ft is equal to 8:4 (8ft to 4ft).

The shortest length of all these pieces is 4 feet.

60 in the ratio of 4:1 = 48:12

12 in the ratio of 2:1 = 8:4

Shortest length is 4.

4

the length were in the ratio 4:1 i.e 48:12

now the 12m rope is cut into 2:1 ratio so the length of two ropes are 8:4

the length of the shortest rope among all these is 4ft

First of all, divide 60 by 5 to get 12, multiply by 4 to get 48. 48+12=60

12/3=4

(2+1=3)

12 feet long rope is the smallest piece

when a 60 feet long rope is cut into two pieces

with lengths that are in the ration 4 : 1.

4x + x = 60

x = 12 feet

4x = 48 feet

the shorter (12 feet) is cut into two pieces in the ratio of: 2 : 1

2x + x = 12

x = 4

the shortest piece is 4 feet...(the other is 8 feet)

Easy problem...try reading the textbook !

Suppose the shorter piece = x

The longer one = 60 - x

The ratio is …… large ……. 4

------- = -------- substituting in terms of x …………………..short …….1

60 - x 4

-------- = ------

x 1

Cross multiply: 60 - x = 4x + x

60 = 5x div by 5

12 = x

Result: The longer piece is 48 ft ( 4x ), the shorter piece is 12 ft

………

60/5=12

12/3=4

total length of rope= 60 ft

it cuts in two pieces with ratio 4:1

let the pieces are 4k ft & k ft

so,

4k ft+k ft=60 ft

i.e. 5k ft= 60 ft

i.e. k= 60/5 =12

so, pieces are of (4*12)ft =48 ft and (1*12)ft=12ft