SOLUTION: Benjamin & Associates, a real estate developer, recently built 210 condominiums in McCall, Idaho. The condos were either two-bedroom units or three-bedroom units. If the total numb

Question 1203898: Benjamin & Associates, a real estate developer, recently built 210 condominiums in McCall, Idaho. The condos were either two-bedroom units or three-bedroom units. If the total number of bedrooms in the entire complex is 537, how many two-bedroom units are there? How many three-bedroom units are there?
Found 4 solutions by MathLover1, math_helper, greenestamps, josgarithmetic:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

let two-bedroom units be and three-bedroom units
if a real estate developer recently built 210 condominiums, we have
...solve for
...eq.1
two-bedroom units have total of bedrooms and three-bedroom units bedrooms
If the total number of bedrooms in the entire complex is ,
....eq.2, substitute

go to
...eq.1, substitute

there are two-bedroom units
there are three-bedroom units

Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!

Let x = number of 3BR units
Let y = number of 2BR units
x + y = 210 (from "... 210 condominiums ...")
3x + 2y = 537 (from "... total number of bedrooms in the entire complex is 537...")
Mulitply the first equation by 2 and subtract that result from the bottom equation:
3x + 2y = 537
-(2x + 2y = 420)
================
x = 117 --> y = 210-117 = 93
Answer:
There are 117 3BR units and 93 2BR units.
Check:
3*117 + 2*93 = 351 + 186 = 537 (total number of BR's checks out)
117 + 93 = 210 (total number of units checks out, note we used this to find y)

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Here is an informal method of solving this kind of problem that gives you good practice in logical reasoning and mental arithmetic.

If all 210 condos were 2-bedroom units, the total number of bedrooms would be 210*2 = 420.
The actual total number of bedrooms is 537, which is 537-420 = 117 more.
Since each 3-bedroom condo has 1 more bedroom than each 2-bedroom condo, the number of 3-bedroom condos must be 117.

ANSWER: 117 3-bedroom condos

Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
210 condominiums
2-bedrooms, and 3-bedrooms, each

d of the 2-br
t of the 3-br

If you try to think about this system without writing steps, maybe see
, which relied on multiplying the d+t equation by 2.

, but question really asks for d.

--------answer
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