SOLUTION: Sales, given in thousands, for a particular company in 1990 were at 140.5 and in 2000 at 180.5. Estimate the sales for the years 1997 and 2003. Let x = 0 correspond to 1990. Using

Algebra ->  Human-and-algebraic-language -> SOLUTION: Sales, given in thousands, for a particular company in 1990 were at 140.5 and in 2000 at 180.5. Estimate the sales for the years 1997 and 2003. Let x = 0 correspond to 1990. Using       Log On


   

Question 189853: Sales, given in thousands, for a particular company in 1990 were at 140.5 and in 2000 at 180.5. Estimate the sales for the years 1997 and 2003. Let x = 0 correspond to 1990. Using the distance formula, find the approximate distance between the values in 1997 and 2003. Explain the difference between using the distance formula and simply subtracting the 2 estimated values.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


In this problem, we need to do Double Interpolation since you got 2 unknown values. (You can do graphing too if you prefer).

Let us see the data given:

A 1990 ----- E 140.5
B 1997 ----- F x
C 2000 ----- G 180.5
B 2003 ----- H y

Solving for x:
%28A-B%29%2F%28A-C%29=%28E-F%29%2F%28E-G%29
%281990-1997%29%2F%281990-2000%29=%28140.5-x%29%2F%28140.5-180.5%29
%28-7%29%2F%28-10%29=%28140.5-x%29%2F%28-40%29
Cross mutiply
%28-7%29%28-40%29=%28-10%29%28140.5-x%29
280=-1405%2B10x
280%2B1405=10x
1685=10x -----> cross%281685%29168.50%2Fcross%2810%29=cross%2810%29x%2Fcross%2810%29
highlight%28red%28x=168.50%29%29 = F, Sales for 1997


Solving for y
%28B-C%29%2F%28B-D%29=%28F-G%29%2F%28F-H%29
%281997-2000%29%2F%281997-2003%29=%28168.5-180.5%29%2F%28168.5-y%29
%28-3%29%2F%28-6%29=%28-12%29%2F%28168.5-y%29
Cross multiply
%28-3%29%28168.5-y%29=%28-6%29%28-12%29
-505.5%2B3y=72
3y=72%2B505.50=577.50
cross%283%29y%2Fcross%283%29=cross%28577.50%29192.50%2Fcross%283%29
highlight%28red%28y=192.50%29%29 = H, Sales for 2003

Distance between values of 1997 & 2003:

H - F = 192.50 - 168.50 = 24, Answer


Thank you,
Jojo