Math

QuestionA company awarded \$3000 in bonuses of \$250 or \$750. If at least one of each was given, how many \$250 bonuses could there be?

Studdy Solution

STEP 1

Assumptions1. The total bonus amount awarded is 3000.Thebonuseswereawardedinamountsof3000. The bonuses were awarded in amounts of 250 or 7503.Atleastone7503. At least one 250 bonus and at least one $750 bonus were awarded

STEP 2

Let's denote the number of 250bonusesas250 bonuses as xandthenumberof and the number of 750 bonuses as yy. We can set up the following equation based on the total bonus amount250x+750y=3000250x +750y =3000

STEP 3

To simplify the equation, we can divide all terms by250x+3y=12x +3y =12

STEP 4

Since we know that at least one 250bonusandatleastone250 bonus and at least one 750 bonus were awarded, we can say that x1x \geq1 and y1y \geq1.

STEP 5

We can start by setting y=1y =1 (the minimum number of 750bonuses)andsolvefor750 bonuses) and solve for x$x +3(1) =12

STEP 6

olve the equation for xxx=123=9x =12 -3 =9So, one possible number of $250 bonuses awarded is9.

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