Chris asked in Science & MathematicsMathematics · 6 months ago

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.

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• 6 months ago

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//

• Ian H
Lv 7
6 months ago

f = 4(14 - f) - 11 = 45 - 4f

f = 9

• ?
Lv 7
6 months ago

> A party has fourteen guests.

TRANSLATION. F+M = 14............[1]

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

TRANSLATION. F = 4M - 11.........[2]

> Find the number of female guests

TRANSLATION. Solve for F

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

F+M = 14...........[1]

F= 4M - 11.........[2]

// Solve by SUBSTITUTION.

// Substitute for F from [2] into [1]

// and solve for M

F+M = 14...........[1]

(4M-11) + M = 14

5M - 11 = 14

5M = 14 + 11

5M = 25

M = 5.................[3]

// Substitute for M from [3] into [2]

// and solve for F

F= 4M - 11.........[2]

F = 4 (5) - 11

F = 20 - 11

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

• 6 months ago

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.

• 6 months ago

F + 11 = 4(14 - F) =>

5F = 56 - 11 =>

F = 9, the number of females.

• 6 months ago

W + M = 14

W = 4M - 11

Substitute

4M - 11 + M = 14

5M = 25

M = 5

Hence

W = 9

• 6 months ago

m + w = 14

w = 4m - 11

m + 4m - 11 = 14

5m = 25

m = 5

m + w = 14

5 + w = 14

w = 9

• 6 months ago

9..................

Source(s): lots of summer school (and my toes)
• 6 months ago

9 female guests with 5 males