Question

One line segment is 5 cm more than 4 times the length of another. The difference in their lengths is 35 cm. How long

are they?
20 cm and 55 cm
10 cm and 40 cm
10 cm and 45 cm
20 cm and 45 cm

Answer 1

10 cm and 45 cm

Explanation:

Let

x -----> the length of one segment

y ----> the length of another segment

we know that

I assume that x > y

x-y=35 -----> equation A

x=4y+5 ----> equation B

substitute equation B in equation A and solve for x

`(4y+5)-y=35\\4y-y=35-5\\3y=30\\y=10\ cm`

Find the value of x

`x=4y+5\\x=4(10)+5\\x=45\ cm`

therefore

The length of the segments are

10 cm and 45 cm