True, false, false, true, true
Step-by-step explanation:
The given equation of the function:
240 = 12x + 8y
where x = number of adults
y = number of children
a) No adult means x = 0
inserting the above into the equation: 240 = 12(0) + 8y
240 = 8y
y = 240/8
y = 30
This means 30 children (students) could go to the zoo
If no adult chaperones were needed, 30 students could go to the zoo: statement is true
b) ten student means y = 10
15 adults means x = 15
inserting the above into the equation:
240 = 12(15) + 8(10)
240 = 180 + 80
180 + 80 = 260
Since 240 is not equal to 260, the statement is false
c) using the values given above: x = 15 and y = 10
240 = 12x + 8y
four more adults = x + 4 = 15 + 4 = 19
12x = 12(19) = 228
The cost of children that will go to the zoo: 240 - 228 = 12
six fewer students = y - 6 = 10 - 6 = 4
8y = 8(4) = 32
Since the cost of children that will go to the zoo (12) is less than the cost of six fewer students (32), there will be no room for 6 fewer students.
The statement is false
d) using the values given above: x = 15 and y = 10
240 = 12x + 8y
two more students go to the zoo = y + 2 = 10+2 = 12
8y = 8(12) = 96
The cost for the adult: 240 - 96 = 144
three fewer adults = x-3 = 15 - 3 = 12
12x = 12(12) = 144
Since the cost for the adult is equal to the cost of three fewer adults, there will be room for three fewer adults.
The statement is true
e) 16 adults go to the zoo means x = 16
6 students can go means y = 6
240 = 12x + 8y
240 = 12(16) + 8(6)
12(16) + 8(6) = 192 + 48 = 240
240 = 240
Since 240 is equal to 240, it means 6 students can go.
The statement is true