Math question from a test today...?

Let x be the number of 2 bedroom houses built.

Let y be the number of 3 bedroom houses built.

They want to build 478 houses total. Using our variables, we get:

x+y = 478

They want to earn exactly 5713000. They get 15000 each for the 2 bedroom houses (x) and 16000 each for the 3 bedroom houses (y). This becomes the following equation:

15000x + 16000y = 5713000

Use the first equation and solve for y:

y= 478 - x

Substitute this in for y in the second equation:

15000x + 16000 ( 478 - x ) = 5713000

Solve this for x and it tells you how many 2 bedroom houses. Plug the answer for x back into the first equation to find y, the number of 3 bedroom houses.

Hope this helps.

Assume that the company is making 'A' 2 bedroom model and 'B' 3 bedroom model.

Total number of houses = 478 can be written as

A + B = 478 ---- Equation (1)

Total profit = 5713000. Profit from 2 bedroom = 15000, profit from 3 bedroom = 16000. This can be written as

15000 * A + 16000 * B = 5713000

Dividing all the terms with 1000 we get

15*A + 16*B = 5713 ---- Equation (2)

Multiplying both sides with 15 the equation (1) above can be re-written as

15*A + 15*B = 7170 ---- Equation (3)

Subtracting equation 3 from equation 2 we get

B = -1457

Substituting the value of B in equation 1 we get

A = 478+1457 = 1935

This means company need to make 1935 2 bedroom houses and -1457 3 bedroom houses.

Note that number of 3 bedroom houses is -ve 1457. This is mathematically OK but practically not at all OK.

I think you have at least one number wrong in there, because it simply doesn't work out in a sensical manner. But here is how you would solve it:

Let's call 2-bedroom houses "A" and 3-bedrooms "B."

A + B = 478

15,000A + 16,000B = 5,713,000

Those are your two equations to begin with. Solve the first for A:

A = 478 - B

Plug that into the second equation:

15,000(478 - B) + 16,000B = 5,713,000

Calculate that out and simplify:

7,170,000 - 15,000B + 16,000B = 5,713,000

7,170,000 + 1,000B = 5,713,000

1,000B = -1,457,000

B = -1,457

Plug that into the first equation:

A + (-1,457) = 478

A = 1935

Check by plugging these numbers into the second equation:

15,000 * 1935 + 16,000 * -1457 = 5,713,000

29,025,000 + -23,312,000 = 5,713,000

5,713,000 = 5,713,000

Obviously you can't build a negative number of houses, so there is a problem with the problem ;)

Two types of houses, x and y, with a total of 478, so

x + y = 478.

Also an equation about profits, with units in $1000:

15x + 16y = 5713.

So multiply the 1st equation by 15 and subtract it from the 2nd:

15x + 16y = 5713

15x + 15y = 7170

---------------------------

.............. y = -1457

Now that's unexpected. Normally, the profit sought for is BETWEEN what you'd get if all the houses were 2 bedroom and what you'd get if all the houses were 3 bedroom, so you need a mixture of the two. But here, if all 478 of the houses were the cheaper 2-bedroom, profits would be 7,170,000. So perhaps you misremembered one of the numbers?

We have 2 variables, so we need two equations to solve this system of equations. On the one hand we have that 478 houses were built. Let's let x be 2 bedroom homes and y be 3 bedroom homes, so:

x + y = 478

For our second equation, we know they want to make 5713k, and that 2 bedrooms yield 15k and 3 yield 16k, so:

15x + 16y = 5713

Now we have our two equations:

01x+01y=0478

15000x+16000y=5713000

Let's multiply the first by -15000:

-15000x-15000y=-7170000

15000x+16000y=5713000

--------------------

1000y = -1457000

y = -1457

Well, obviously something is wrong in your problem... also, you can tell this since the need to build 478 homes making at least 15,000 on each one, that is a minimum of 7,170,000 which is more than they want to make. I think you have some of the numbers wrong.

Was it a trick question?

If they were going to build 478 houses and make $5,713,000 in profit, the average profit they would make per house is $11,951.88. This number is less than the profit of either house style. So they can't build 478 houses of either style (or a combination of either style) and make exactly $5,713,000.

They have to build fewer than 478 houses to profit exactly $5,713,000.

Another way to look at it: if they build 478 houses at the minimum profit per house ($15,000 / 2 br house), they would profit $7,170,000. This is more than the profit that they are seeking to make exactly.

Yet another way to look at it: if all houses built were 2 bedroom houses, they would have to build 381 (rounded) houses to reach their desired profit ($5713000/$15000). If they were all 3 bedroom houses, they would build 357 (rounded) to reach their desired profit ($5713000/$15000). So if they wanted to only reach their desired profit with a combination of house types, they would have to build between 357 and 381 houses.

Well, I gave it a try - several times in fact - and then I got an idea:

Divide 5,713,000 by the total number of houses, 478 - and it's $11,951.88 average profit for each house sold. This clown wants to make $15,000 and $16,000 respectively.

AIN'T GONNA HAPPEN.

i've been trying to solve this problem and i dont think you can. if you divide the expected profit of $5713000 by the number of housed, 478, you get $11,951.... so that means you have to make an avg profit of that. but since you make more on each house, there is no way. these numbers must be wrong.

5,713,000 / 15,000 (the cheapest way to make the most houses) = <478 houses.

Using the cheapest houses available, you can only make 380 some houses, there is no way given the information here that you can make 478 houses.

let x be the no of 2 bed room houses and y be three bed room houses.

there fore

x + y =478

15000x +16000y = 5713000

solving these simultaneous equations

will give you the combinations of houses.

but in the question there must be an error if u solve the above equation you ll get unrealistic answer(x=1935,y=-1457)