Question

question
bilquis is preparing many gifts for a family holiday party. each gift must either be wrapped with wrapping paper or prepared in a gift bag. bilquis can wrap a single gift in 4.5 minutes and she can do a giftbag in 2 minutes. bilquis prepared a total 21 gifts in 79.5 minutes. write a system of equations that could be used to determine the number of gifts bilquis wrapped and the number of giftbags she prepared. define the variables that you use to write the system.
answer attempt 1 out of 2
let
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let
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system of equations:

Explanation:

Step1: Define variables

Let $x$ = number of wrapped gifts, $y$ = number of giftbag gifts

Step2: Total gifts equation

Total gifts: $x + y = 21$

Step3: Total time equation

Total time: $4.5x + 2y = 79.5$

Step4: Solve variable $x$

Rearrange first eq: $y = 21 - x$. Substitute into second eq:
$4.5x + 2(21 - x) = 79.5$
$4.5x + 42 - 2x = 79.5$
$2.5x = 79.5 - 42$
$2.5x = 37.5$
$x = \frac{37.5}{2.5} = 15$

Step5: Solve variable $y$

Substitute $x=15$ into $x + y = 21$:
$15 + y = 21$
$y = 21 - 15 = 6$

Answer:

Let $x$ = number of wrapped gifts, Let $y$ = number of giftbag gifts
System of Equations:
$x + y = 21$
$4.5x + 2y = 79.5$
Number of wrapped gifts: 15, Number of giftbag gifts: 6