Math question from a test today...?

Question

I am completely stumped on this question. It's from a test I already did, so this is for curiosity, not for someone else to do my homework.

If a company is building 478 houses and stand to profit $15,000 from a 2 bedroom model and $16,000 from a three bedroom model, and they are seeking to make exactly $5,713,000 in profit, how many of each house do they need to make?

Could someone show me how to solve this. I don't even care if you give me an answer, just let me know how to do it myself.... The answer must be numbers, not formulas. I just don't get how to solve it.

The reason that I was confused is to do with the numbers... I agree it doesn't make sense I just thought I was missing something.

I also had a complete brain lapse... the first person that anwsered this question, gave me the equation I was looking for. Thanks!!

Answer 1

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.

Answer 2

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.

Answer 3

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 ;)

Answer 4

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?

Answer 5

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.

Answer 6

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.

Answer 7

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.

Answer 8

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.

Answer 9

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.

Answer 10

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)