Problem:
A group of children (x) and adults (y) are waiting to ride an elevator. The elevator has a maximum capacity of 8 people. It also has a weight limit of 1000 kg. Supposed that each child weighs 40 kg and each adult weighs 100 kg.
Graph the system of inequalities showing the possible number of children and adult that can ride the elevator at the same time. Determine the number of children and adults that can ride the elevator.
Solution:
x = group of children
y = group of adults
maximum capacity = 8 people
weight limit = 1000kg
weight of each (x) children = 40kg
weight of each (y) adults = 100kg
Equation 1:
x + y ≤ 8
Equation 2:
40x + 100y ≤ 1000
if x = 0
x + y = 8
0 + y = 8
y = 8
(0, 8) ; y intercept
if y = 0
x + y = 8
x + 0 = 8
x = 8
(8, 0) ; x intercept
if x = 0
40x + 100y = 1000
40(0) + 100y = 1000
0 + 100y = 1000
y = 1000/100
y = 10
(0, 10) ; y intercept
if y = 0
40x + 100y = 1000
40x + 100(0) = 1000
40x + 0 = 1000
40x = 1000
x = 1000/40
x = 25
(25, 0) ; y intercept
Plot these points on the graph
For equation 1:
x + y ≤ 8
(0, 8) ; y intercept
(8, 0) ; x intercept
For equation 2:
40x + 100y ≤ 1000
(0, 10) ; y intercept
(25, 0) ; y intercept
Graph the system of inequalities showing the possible number of children and adult that can ride the elevator at the same time.
Please see attached.
Determine the number of children and adults that can ride the elevator.
if (1, 1)
x + y ≤ 8
1 + 1 ≤ 8
2 ≤ 8 ; true
if (1, 1)
40x + 100y ≤ 1000
40(1) + 100(1) ≤ 1000
40 + 100 ≤ 1000
140 ≤ 1000 ; true
if (7, 1)
x + y ≤ 8
7+ 1 ≤ 8
8 ≤ 8 ; true
if (7, 1)
40x + 100y ≤ 1000
40(7) + 100(1) ≤ 1000
280 + 100 ≤ 1000
380 ≤ 1000 ; true
if (1, 7)
x + y ≤ 8
1 + 7 ≤ 8
8 ≤ 8 ; true
if (1, 7)
40x + 100y ≤ 1000
40(1) + 100(7) ≤ 1000
40 + 700 ≤ 1000
740 ≤ 1000 ; true
you can try and substitute these values to the equation to prove that the area bounded by green shade on the attached file is the ordered pair or the solution to both equations x + y ≤ 8 and 40x + 100y ≤ 1000
(1, 1)
(1, 2)
(1, 3)
(1, 4)
(1, 5)
(1, 6)
(1, 7)
(2, 1)
(2, 2)
(2, 3)
(2, 4)
(2, 5)
(2, 6)
(3, 1)
(3, 2)
(3, 3)
(3, 4)
(3, 5)
(4, 1)
(4, 2)
(4, 3)
(4, 4)
(5, 1)
(5, 2)
(5, 3)
(6, 1)
(6, 2)
(7, 1)
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