A party has fourteen guests. The number of women is eleven less than four times the number of males. Find the number of female guests.

Relevance

party = 14

w = 4m - 11

w + m = 14

w = 4m - 11

4m - 11 + m = 14

5m - 11 = 14

5m = 14 + 11

5m = 25

m = 5 -------------- number of males is 5 answer//

w = 4m - 11

w = 4(5) - 11

w = 9 -----------------number of woman is 9 answer//

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• f = 4(14 - f) - 11 = 45 - 4f

f = 9

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• > A party has fourteen guests.

TRANSLATION. F+M = 14............

> The number of women is eleven less than four times the number of males.

TRANSLATION. F = 4M - 11.........

> Find the number of female guests

TRANSLATION. Solve for F

// You have a system of 2 equations and 2 unknowns.

F+M = 14...........

F= 4M - 11.........

// Solve by SUBSTITUTION.

// Substitute for F from  into 

// and solve for M

F+M = 14...........

(4M-11) + M = 14

5M - 11 = 14

5M = 14 + 11

5M = 25

M = 5.................

// Substitute for M from  into 

// and solve for F

F= 4M - 11.........

F = 4 (5) - 11

F = 20 - 11

F = 9......................ANS

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• x = male, y = female

x + y = 14 thus x = 14 - y

y = 4x - 11

sub x from first eqtn

y = 4(14 - y) - 11

y = 56 - 4y - 11

y = -4y + 45

5y = 45

y = 45 / 5 = 9 women

women + men = 14 thus 5 men.

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• F + 11 = 4(14 - F) =>

5F = 56 - 11 =>

F = 9, the number of females.

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• W + M = 14

W = 4M - 11

Substitute

4M - 11 + M = 14

5M = 25

M = 5

Hence

W = 9

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• m + w = 14

w = 4m - 11

m + 4m - 11 = 14

5m = 25

m = 5

m + w = 14

5 + w = 14

w = 9

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• 9..................

Source(s): lots of summer school (and my toes)
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• 9 female guests with 5 males

• King Leo
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