Number line

[cartera]

R,T,P,S are points in a number line，RT=(1/3)RP, TP=(2/5)TS, R= -16，S=8, what is the value of P?

R(-16)----------(T)---------------(P)---------------------------S(8)

[krovvidy]

First, you can clearly see that RS = 8-(-16) = 24

Second, RS = RT + TS
i.e., 24 = RT + (5/2)TP ... [since TP = (2/5)TS]
i.e., 24 = RT + (5/2)(RP-RT) ... [since RP = RT + TP]
i.e., 24 = (1/3)RP + (5/2)(RP-(1/3)RP) ... [since RT = (1/3)RP]
i.e., 24 = (1/3)RP + (5/3)RP
i.e., 24 = 2RP
i.e., RP = 12
i.e., 12 = -16 - P
Therefore P = -28

HTH

[selytch]

-28 cannot be true since it is less than -16 (the leftmost point).

scale1: R--1/3---T---2/3----------P------------------S
scale2: R--------T---2/5----------P-------3/5--------S

(2/3)/(2/5)=10/6 (conversion factor from lower to upper scale)
personal statement (on upper scale)=(3/5)*(10/6)=1
RS=1/3x+2/3x+1x=24
x=12
P=1x+(-16)
P=-4

(krovvidy meant +P i suppose...)

Official Answer?

[krovvidy]

You're right ... it should've been +P and hence P = -4. My bad!

-28 cannot be true since it is less than -16 (the leftmost point).

scale1: R--1/3---T---2/3----------P------------------S
scale2: R--------T---2/5----------P-------3/5--------S

(2/3)/(2/5)=10/6 (conversion factor from lower to upper scale)
personal statement (on upper scale)=(3/5)*(10/6)=1
RS=1/3x+2/3x+1x=24
x=12
P=1x+(-16)
P=-4

(krovvidy meant +P i suppose...)

Official Answer?

[ahsan400]

-28 cannot be true since it is less than -16 (the leftmost point).

scale1: R--1/3---T---2/3----------P------------------S
scale2: R--------T---2/5----------P-------3/5--------S

(2/3)/(2/5)=10/6 (conversion factor from lower to upper scale)
personal statement (on upper scale)=(3/5)*(10/6)=1
RS=1/3x+2/3x+1x=24
x=12
P=1x+(-16)
P=-4

(krovvidy meant +P i suppose...)

Official Answer?

Hello Selytch,
Can you please explain how did you convert the factors from lower to upper scale?