A group of 148 people is spending five days at a summer camp.
The cook ordered 12 pounds of food for each adult and 9 pounds of food for each child.
A total of 1, 410 pounds of food was ordered.
What is the total number of adults and total number of children in the group?
A group of 148 people is spending five days at a summer camp.
Let x represents the adult and y represents the children:
x + y = 148 ................... equ 1
The cook ordered 12 pounds of food for each adult and 9 pounds of food for each child.
A total of 1, 410 pounds of food was ordered.
12 x + 9 y = 1410 .......... equ 2
Solving :
x + y = 148 ................... equ 1 x 9 = 9x + 9y = 1332 ------------- equ 3
12 x + 9 y = 1410 .......... equ 2
equ 3 - equ 2:
9 x - 12 x = 1332 - 1410
- 3x = -78
Divide both sides by -3
x = 26 adults
put x = 26 in equ 1
x + y = 148
26 + y = 148
y = 148 - 26
y = 122 children
Conclusion : x = 26 adults , y = 122 children