Question 1150280: Town A and Town B were located close to each other, and recently merged into one city. Town A had a population with 6% Hispanics. Town B had a population with 12% Hispanics. After the merge, the new city has a total of 4800 residents, with 10.5% Hispanics. How many residents did Town A and Town B used to have?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Town A and Town B were located close to each other, and recently merged into one city.
Town A had a population with 6% Hispanics.
Town B had a population with 12% Hispanics.
After the merge, the new city has a total of 4800 residents, with 10.5% Hispanics.
How many residents did Town A and Town B used to have?
:
let a = no. of residents in town A
let b = no. of residents in town B
:
Two equations
a + b = 4800
a = (4800-b)
and
.06a + .12b = .105(4800)
.06a + .12b = 504
replace a with (4800-b)
.06(4800-b) + .12b = 504
288 - .06b + .12b = 504
.06b = 504 - 288
.06b = 216
b = 216/.06
b = 3600 in town B
then
4800 - 3600 = 1200 in Town A
:
;
See if that checks out; find how many in each town.
.06(1200) = 72
.12(3600) = 432
-----------------
total Hisp. 504 in both towns
|
|
|
