Question

A segment is divided into two parts having lengths in a ration of 7:2. Find the lengths of each part, if the difference between the segment lengths is 15 inches.

Answer 1

@Shadow

Answer 2

Hey, let's take the lengths of these two segments, call them x and y.
Say x is the bigger of the two. So, we know that x = 7.2y
We also know that x-y = 15
Now we have a system of equations. If you combine them, you can solve for y, then use that to solve for x

Answer 3

no its 7x and 2x cus if the ratio is 7:2

Answer 4

Oh, yes, I misread 7:2 as 7.2 I must be getting old, rip
But yeah, in that case the first equation would be 2x = 7y

Answer 5

ok....

Answer 6

Yup, so then you can simplify that to x = 3.5y
Then we take our other equation, x - y = 15. We can rewrite it as x = y + 15.
And now we have two equations that tell us x is equal to something. Well, if a=b and a=c, then b=c. So, we can combine these two equations like
3.5y = y + 15
Now we can isolate y
2.5y = 15
y = 15/2.5 = 6
Now, since y = 6, and x - y = 15, x must be 21
Does that match up? Well, 21 * 2 is 42. And 6 * 7 is 42. So, our equations check out.

Answer 7

i dont think you can simplify 7y=2x to x=3.5y cus of the two different variables

Answer 8

@SmokeyBrown

Answer 9

Oh, nah, it's cool. The variables aren't actually interacting with each other, like if we tried to add or subtract them. We're just dividing the coefficients (the numbers multiplying the variables)

Answer 10

ok

Answer 11

but the difference of both length is 15

Answer 12

Yeah, that's true. So, x - y = 15, if x is larger.
And the results we got match, since 21 - 6 does give a difference of 15

Answer 13

ok