Answered

A Spanish class has a total of 35 students. The number of females is 9 less than the number of males. How many males and how many females are in the class?
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Answer :

Answer:

There are 13 females in the class.

Step-by-step explanation:

Setting Up a System of Equations

A system of equations can be written to model each sentence.

If a Spanish class consists of males, m and females, f then,

[tex]m+f=35[/tex].

If the number of f is 9 less than m then f can be written in terms of m or,

[tex]f=m-9[/tex].

Solving for f Stragetically

We substitute the second equation of f into the first equation but, that solves for m since all the terms on the left side would be in terms of m.

Although we can proceed with this step, and plug in the solved m value into the second equation to find f, a quicker method can be used.

We can rearrange the second equation to have m in terms of f so that when we plug in the second equation in the first, we have the first equation all in terms of f.

[tex]f=m-9\\\\\Rightarrow f+9 = m[/tex]

Inserting the modified second equation into the initial equation,

                                    [tex](f+9)+f=35[/tex]

                                       [tex]2f+9=35[/tex]

                                          [tex]2f=26[/tex]

                                           [tex]f=13[/tex].