Word Translation Ch 1 Q 8

[KC]

The problem states:
Carla cuts a 70-inch piece of ribbon into 2 pieces. If the 1st piece is 5 inches more than 1/4 as long as the 2nd piece, how long is the longer piece of ribbon?

Here is how I answered it:

step 1:
x= 1st piece of ribbon y=2nd piece of ribbon

step 2:
x+y = 70 x= 5 + y/4 + y

step 3:
5 + y/4 + y = 70
5y = 60
y = 12

step 4:
x + 12 = 70
x = 58 = the longer piece of ribbon

The answer key has something completely different in step 3 than what I have. They eventually got the answer to be 52. I am just not sure how they got 5y = 260 in step 3 and where they '20' came from in that equation. I do understand that what I got is wrong, because if I plus the #'s back into the original equation, it doesn't match up. Just not sure how to arrive at the correct answer. [/b]

[KC]

I just realized that you have to multiply by 4 on both sides. Guess I just need to take a longer look at these problems!

[blue_lotus]

step 1:
x= 1st piece of ribbon y=2nd piece of ribbon

step 2:
x= 5 + y/4 --------- 1


Also x+y=70 => x = 70 -y --------------2

from 1 & 2
5+y/4 = 70 -y

(20 + y)/4 = 70-y

20 + y = 280 - 4y

take Y to the Left hand side
20 + 5y = 280

Take 20 to the RHS

5y = 280 -20

5y = 260

y = 52

since x + y = 70
x = 70 - 52 = 18

Therefore Longest piece is 52

[StaceyKoprince]

Excellent! Glad you figured it out for yourself - that's always the best way to learn! :)