Math problem from a test today...?

It's a system of equations.

Let x be the number of 2bedroom houses. Than 478 -x is the number of 3-bedroom houses.

x(15,000) + (478 - x) (16,000) = 5713000

15000x + (478)(16000) - 16000x = 5713000

-1000x = 5713000 - (478)(16000)

x = 5713000 - (478)(16000) / -1000

so that's the number of 2b houses, then subtract from 478 for the number of 3b houses

First of all, this problem is impossible as it is written. If they are building 478 houses, and making either 15,000 or 16000 profit from each, the least amount of profit they could make would be over 7 million (15000*478). I think you have the total profit wrong.

Anyway,

These types of problems are called systems of equations. You will have 2 variables, in this case 2 bedroom houses and 3 bedroom houses, and will be given enough information to make two equations.

we'll let x=2 bedroom houses and y = 3 bedroom houses

you know that the company will build 478 total houses, so x+y=478

and you know that they want to make a total profit of 5,713,000 from the sale of the houses.

since they make 15,000 profit for every 2 bedroom house, and 16,000 from every 3 bedroom house,

the total profit can be written as

15,000x + 16,000y = 5,713,000

now that you have 2 equations, you can solve

x+y=478

15,000x+16,000y=5,713,000

from the first equation, you can get that y=478-x

now take that and substitute it into the second equation, so that you only have 1 variable to solve for

15000x + 16000(478-x) = 5713000

15000x + 7648000 - 16000x = 5713000

-1000x = -1935000

x=1935

plug that back into the first equation to find the value of y

x+y=478

1935+y=478

y=-1457

So you can see why your numbers are wrong, but if they were right, this is how you work systems of equations.

let X = number of 2 bedroom houses

let Y = no. 3 bedroom houses

X + Y = 478

15000X + 16000Y = 5713000

Solving these equations by elimination method will give you a negative number for Y. Which is not possible. The number of houses can't be negative. This problem is stated incorrectly.

You've made a mistake somewhere in your numbers.

If we take $5,713,000 / 478 houses, then the price of each house would be $11,951.88, which is MUCH LESS than the SELLING price of $15,000 and $16,000 respectively.

Could the profit from the houses be $1,500 and $1,600 instead?

yea set this up as a system of equations problem... seems like the easiest choice to me. remember both substitution as well as addition elimination when doing these.