QuestionA company awarded bonuses totaling \$3000 in \$250 or \$750 amounts. If both types were given, how many \$250 bonuses could there be?

Studdy Solution

STEP 1

Assumptions1. The total bonus amount is $\$3000$ . The bonuses were awarded in amounts of $\$250$ or $\$750$
3. At least one $\$250$ bonus and at least one $\$750$ bonus were awarded

STEP 2

Let's denote the number of $\$250$ bonuses as $x$ and the number of $\$750$ bonuses as $y$ . We can write the equation that represents the total bonus amount.
$250x +750y =3000$

STEP 3

We can simplify the equation by dividing all terms by250.
$x +3y =12$

STEP 4

Since we know that at least one $\$250$ bonus and at least one $\$750$ bonus were awarded, we can say that $x \geq1$ and $y \geq1$ .

STEP 5

We can start by assuming the minimum value for $y$ , which is1. Substitute $y =1$ into the equation.
$x +3(1) =12$

STEP 6

olve the equation for $x$ .
$x =12 -3 =9$ So, one possible number of $\$250$ bonuses awarded is9.

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QuestionA company awarded bonuses totaling \$3000 in \$250 or \$750 amounts. If both types were given, how many \$250 bonuses could there be?

Studdy Solution

STEP 1

Assumptions1. The total bonus amount is $\$3000$ . The bonuses were awarded in amounts of $\$250$ or $\$750$
3. At least one $\$250$ bonus and at least one $\$750$ bonus were awarded

STEP 2

Let's denote the number of $\$250$ bonuses as $x$ and the number of $\$750$ bonuses as $y$ . We can write the equation that represents the total bonus amount.
$250x +750y =3000$

STEP 3

We can simplify the equation by dividing all terms by250.
$x +3y =12$

STEP 4

Since we know that at least one $\$250$ bonus and at least one $\$750$ bonus were awarded, we can say that $x \geq1$ and $y \geq1$ .

STEP 5

We can start by assuming the minimum value for $y$ , which is1. Substitute $y =1$ into the equation.
$x +3(1) =12$

STEP 6

olve the equation for $x$ .
$x =12 -3 =9$ So, one possible number of $\$250$ bonuses awarded is9.

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QuestionA company awarded bonuses totaling \$3000 in \$250 or \$750 amounts. If both types were given, how many \$250 bonuses could there be?

Studdy Solution

STEP 1

Assumptions1. The total bonus amount is $3000\$3000$3000 . The bonuses were awarded in amounts of $250\$250$250 or $750\$750$7503. At least one $250\$250$250 bonus and at least one $750\$750$750 bonus were awarded

STEP 2

Let's denote the number of $250\$250$250 bonuses as xxx and the number of $750\$750$750 bonuses as yyy. We can write the equation that represents the total bonus amount.250x+750y=3000250x +750y =3000250x+750y=3000

STEP 3

We can simplify the equation by dividing all terms by250.x+3y=12x +3y =12x+3y=12

STEP 4

Since we know that at least one $250\$250$250 bonus and at least one $750\$750$750 bonus were awarded, we can say that x≥1x \geq1x≥1 and y≥1y \geq1y≥1.

STEP 5

We can start by assuming the minimum value for yyy, which is1. Substitute y=1y =1y=1 into the equation.x+3(1)=12x +3(1) =12x+3(1)=12

STEP 6

olve the equation for xxx.x=12−3=9x =12 -3 =9x=12−3=9So, one possible number of $250\$250$250 bonuses awarded is9.

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Assumptions1. The total bonus amount is $\$3000$ . The bonuses were awarded in amounts of $\$250$ or $\$750$
3. At least one $\$250$ bonus and at least one $\$750$ bonus were awarded

Let's denote the number of $\$250$ bonuses as $x$ and the number of $\$750$ bonuses as $y$ . We can write the equation that represents the total bonus amount.
$250x +750y =3000$

We can simplify the equation by dividing all terms by250.
$x +3y =12$

Since we know that at least one $\$250$ bonus and at least one $\$750$ bonus were awarded, we can say that $x \geq1$ and $y \geq1$ .

We can start by assuming the minimum value for $y$ , which is1. Substitute $y =1$ into the equation.
$x +3(1) =12$

olve the equation for $x$ .
$x =12 -3 =9$ So, one possible number of $\$250$ bonuses awarded is9.