The sales manager of a company awarded a total of \$3000$3000dollar sign, 3000 in bonuses to the most productive salespeople. the bonuses were awarded in amounts of \$250$250dollar sign, 250 or \$750$750dollar sign, 750. if at least one \$250$250dollar sign, 250 bonus and at least one \$750$750dollar sign, 750 bonus were awarded, what is one possible number of \$250$250dollar sign, 250 bonuses awarded

Let number of $250 bonus = x

Let number of $750 bonus = 7

Given that total bonus amount awarded is $3000. So we can write equation:

250x+750y=3000

750y=3000-250x

Given that both type of bonus awarded are at least one.

So that means y>1 and x>1

Now we have to find any one possible solution.

Number of awards can only be whole numbers so we can plug x=2,3,4,... to see which one satisfies above equation and gives x as whole number.

I found that x=3 is working good.

at x=3, we get:

y=3

Hence final answer is given by:

Number of $250 bonus = 3

and number of $750 bonus = 3

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

b