5 c + 7 s + 9 a = 6100
c + s + a = 900
a = .5 (c+s) or 2a - c - s = 0
============================
add two and three
3 a = 900
so
a = 300
c+s = 600 so s = 600 - c
3 c + 7 s + 2700 = 6100
3 c + 7(600-c) = 3400
3 c + 4200 - 7 c = 3400
4 c = 800
c = 200
A theater has a seating capacity of 900 and charges $5 for children, $7 for students, and $9 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $6100. How many children attended the show?
3 answers
a = adults
c = childrens
s = students
With a full audience:
a + c + s = 900
There were half as many adults as children and students combined mean:
a = ( s + c ) / 2
Replace this in equation:
a + c + s = 900
( s + c ) / 2 + c + s = 900 Multiply both sides by 2
s + c + 2 c + 2 s = 1,800
3 c + 3 s = 1,800 Divide both sides by 3
c + s = 600
The receipts totaled $6,100 mean:
$9 * adults + $7 * students + $5 * chidrens= $6,100
$9 * a + $7 * s + $5 * c = $6,100
9 a + 7 s + 5 c = 6,100
Replace a = ( s + c ) / 2 in this equation.
9 * ( s + c ) / 2 + 7 s + 5 c = 6,100 Multiply both sides by 2
9 ( s + c ) + 2 * 7 s + 2 * 5 c = 2 * 6,100
9 s + 9 c + 14 s + 10 c = 12,200
23 s + 19 c = 12,200
Now you must solve 2 equations with 2 unknow:
c + s = 600
23 s + 19 c = 12,200
Try that.
The solutions are : c = 400 , s = 200
400 childrens
200 students
Proof:
a = ( s + c ) / 2
a = ( 400 + 200 ) / 2 = 600 / 2 = 300
300 adults
$9 * a + $ 7 * s + $5 * c = $6,100
$9 * 300 + $ 7 * 200 + $5 * 400 = $6,100
$2,700 + $1,400 + $2,000 = $6,100
$6,100 = $6,100
c = childrens
s = students
With a full audience:
a + c + s = 900
There were half as many adults as children and students combined mean:
a = ( s + c ) / 2
Replace this in equation:
a + c + s = 900
( s + c ) / 2 + c + s = 900 Multiply both sides by 2
s + c + 2 c + 2 s = 1,800
3 c + 3 s = 1,800 Divide both sides by 3
c + s = 600
The receipts totaled $6,100 mean:
$9 * adults + $7 * students + $5 * chidrens= $6,100
$9 * a + $7 * s + $5 * c = $6,100
9 a + 7 s + 5 c = 6,100
Replace a = ( s + c ) / 2 in this equation.
9 * ( s + c ) / 2 + 7 s + 5 c = 6,100 Multiply both sides by 2
9 ( s + c ) + 2 * 7 s + 2 * 5 c = 2 * 6,100
9 s + 9 c + 14 s + 10 c = 12,200
23 s + 19 c = 12,200
Now you must solve 2 equations with 2 unknow:
c + s = 600
23 s + 19 c = 12,200
Try that.
The solutions are : c = 400 , s = 200
400 childrens
200 students
Proof:
a = ( s + c ) / 2
a = ( 400 + 200 ) / 2 = 600 / 2 = 300
300 adults
$9 * a + $ 7 * s + $5 * c = $6,100
$9 * 300 + $ 7 * 200 + $5 * 400 = $6,100
$2,700 + $1,400 + $2,000 = $6,100
$6,100 = $6,100
A theater is presenting a program on drinking and driving for students and their parents or other responsible adults. The proceeds will be donated to a local alcohol information center. Admission is $ 10.00 for adults and $ 5.00 for students. However, this situation has two constraints: The theater can hold no more than 210 people and for every two adults, there must be at least one student. How many adults and students should attend to raise the maximum amount of money?
To raise the maximum amount of money,
nothing adults and
nothing students should attend.
To raise the maximum amount of money,
nothing adults and
nothing students should attend.
1 answer