Let shorter part be S inches long. Then larger part (L) is 4S inches long and sum of the piece lengths = S +4S = 5S = 60 inches. Then (S, L) = (12, 48).

The first part  measures 48 inches and the other part 12 inches.

A piece of wire is 60 inches is cut into two pieces with ratio 1part:4parts. total length is 5parts.

5x = 60,   x=60/5, x=12 inches.

A 60 in. piece of wire is to be cut into 2 parts,

x + y = 60

one part being four times the length of the other.

x = 4y

Substitute into x + y = 60

4y + y = 60

5y = 60

y = 12

Substitute into x = 4y

x = 12 x 4

x = 48

ANS 12 inches and 48 inches.

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Or

A 60 in. piece of wire is to be cut into 2 parts, one part being four times the length of the other.

-The two pieces are related by a ratio of 4 : 1 ie 5 parts

1 part = 60/5 = 12 inches

4 parts = 12 inches x 4 = 48 inches

ANS 12 inches and 48 inches

Let parts be of length x ins and 4x

x + 4x = 60

5x = 60

x = 12

so x=12 and 4x = 4*12=36

The lengths are 48 inches and 12 inches

:-

Let parts be of length x ins and 4x ins

5x = 60

x = 12

Lengths are 12 ins and 48 ins

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10 and the number 50

Sounds like a problem for you to solve while I sit back and watch your little brain implode from the stress