Answer:
[tex]\textsf{Let }\boxed{x}=\boxed{\textsf{number of single gifts wrapped.}}[/tex]
[tex]\textsf{Let }\boxed{y}=\boxed{\textsf{number of gift bags prepared.}}[/tex]
System of Equations:
[tex]\boxed{x + y = 21}[/tex]
[tex]\boxed{4.5x + 2y = 79.5}[/tex]
Step-by-step explanation:
Given information:
- Bilquis can wrap a single gift in 4.5 minutes.
- Bilquis can prepare a gift bag in 2 minutes.
- Bilquis prepared a total of 21 gifts in 79.5 minutes.
Define the variables:
Let x = number of single gifts wrapped.
Let y = number of gift bags prepared.
Create two equations with the given information and defined variables:
[tex]\begin{cases}x + y = 21\\4.5x + 2y = 79.5 \end{cases}[/tex]
To solve the system of equations, rewrite the first equation to make x the subject:
[tex]\implies x=21-y[/tex]
Substitute this into the second equation and solve for y:
[tex]\implies 4.5(21-y)+2y=79.5[/tex]
[tex]\implies 94.5-4.5y+2y=79.5[/tex]
[tex]\implies 94.5-2.5y=79.5[/tex]
[tex]\implies -2.5y=-15[/tex]
[tex]\implies y=6[/tex]
Substitute the found value of y into the first equation and solve for x:
[tex]\implies x+6=21[/tex]
[tex]\implies x=15[/tex]
Therefore, the solution to the system of equations is:
- x = 15 → Bilquis wrapped 15 single gifts.
- y = 6 → Bilquis prepared 6 gift bags.
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