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As the coronavirus is spreading at a rapid pace and the flu season is right around the corner. Dr. Oh is in charge of providing vaccinations to fight the virus. The covid 19 vaccine has 12 doses while the flue vaccine has 6 doses. So far she has given 28 vaccinations that had a total of 222 doses. how many covid 19 and flu vaccines has she given out so far?i need help with systems if equations. I have made a real world problem to model systems if equations and I got the answer too. I just need someone to tell me if the problem is correct and if the answer is correct. I also want to know if my problem makes sense.

Respuesta :

Answer:

9 covid-19 vaccines and 19 flu vaccines.

Explanation:

Let the number of covid-19 vaccines given out = x

Let the number of flu vaccines given out = y

In total, she has given out 28 vaccinations, therefore:

[tex]\begin{gathered} x+y=28 \\ \implies x=28-y \end{gathered}[/tex]

• The covid-19 vaccine has 12 doses.

,

• The flu vaccine has 6 doses.

,

• Total number of doses = 222

This gives us:

[tex]12x+6y=222[/tex]

We solve the system of equations by substitution.

[tex]\begin{gathered} 12x+6y=222 \\ 12(28-y)+6y=222 \\ 336-12y+6y=222 \\ -6y=222-336 \\ -6y=-114 \\ y=-\frac{114}{-6} \\ y=19 \end{gathered}[/tex]

Recall that:

[tex]\begin{gathered} x=28-y \\ =28-19 \\ =9 \end{gathered}[/tex]

Therefore, she has given out 9 covid-19 vaccines and 19 flu vaccines.