All categories

3 years ago

Two positive numbers have a sum of 8 and their product is equal to the larger number plus 10

Mathematics

1 answer:

IRISSAK [1]3 years ago

5 0

Answer:

There are 2 sets of numbers that work...

x = 3, y = 5

and

x = 6, y = 2

Step-by-step explanation:

Let x be one number, and let y be the other number. We have 2 equations...

x + y = 8 (two positive numbers have a sum of 8)

xy = y + 10 (their product is equal to the larger number plus 10)

solve the first equation for y, and substitute that into the second equation...

y = 8 - x

x(8 - x) = 8 - x + 10

now solve for x...

8x - x² = 18 - x

This is a quadratic, so get everything to one side so it's equal to zero...

-x² + 9x - 18 = 0 (add x and subtract 18 from both sides)

Now solve for x...

x² - 9x + 18 = 0 (divide both sides by -1)

(x - 6)(x - 3) = 0 (factor)

x - 6 = 0 becomes x = 6 (add 6 to both sides)

and

x - 3 = 0 becomes x = 3 (add 3 to both sides

If x is 3, then y = 5 (3 + 5 is 8, and 3(5) = 5 + 10, both equations hold up)

If x is 6, then y = 2 (6 + 2 is 8, and 6(2) = 2 + 10, both equation hold up)

You might be interested in

A catering company prepared and served 300 meals at an anniversary celebration last week using eight workers. The week before, s

swat32

Answer:

II case.

Step-by-step explanation:

Given that a catering company prepared and served 300 meals at an anniversary celebration last week using eight workers.

The week before, six workers prepared and served 240 meals at a wedding reception.

Productivity is normally measured by number of outputs/number of inputs

Here we can measure productivity as

no of meals served/no of workers

In the I case productivity = $\frac{300}{8} \\=37.5$

In the II case productivity = $\frac{240}{6} \\=40$

Obviously II case productivity is more as per worker 40 meals were served which is more than 37.5 meals per worker in the I case.

3 0

3 years ago

Fed [463]

I’m pretty sure it is d

7 0

3 years ago

Read 2 more answers

Mathew has 18 sets of baseball cards. Eachset has 12 cards. About how many baseball cards does mathew have

maksim [4K]

it is 216 baseball cards

3 0

4 years ago

Solve both of these please.

MAVERICK [17]

Answer:

( n + 4 ) - 9

- n - 4 - 9

- n - 13

40 = x - 1

- x = - 1 + 40

- x = 39

Step-by-step explanation:

I duno if this is right...

8 0

3 years ago

A church rings its bells every 15 minutes, the school rings its bells every 20 minutes and the day care center rings its bells e

ankoles [38]

Answer:

As few as just over 345 minutes (23×15) or as many as just under 375 minutes (25×15).

Imagine a simpler problem: the bell has rung just two times since Ms. Johnson went into her office. How long has Ms. Johnson been in her office? It could be almost as short as just 15 minutes (1×15), if Ms. Johnson went into her office just before the bell rang the first time, and the bell has just rung again for the second time.

Or it could be almost as long as 45 minutes (3×15), if Ms. Johnson went into her office just after the bells rang, and then 15 minutes later the bells rang for the first time, and then 15 minutes after that the bells rang for the second time, and now it’s been 15 minutes after that.

So if the bells have run two times since Ms. Johnson went into her office, she could have been there between 15 minutes and 45 minutes. The same logic applies to the case where the bells have rung 24 times—it could have been any duration between 345 and 375 minutes since the moment we started paying attention to the bells!

Step-by-step explanation:

7 0

3 years ago