Question

A group of 148 people spending 5 days out of summer camp the Cook ordered 12 lb of food for each adult and 9 pounds of food for each child. A total of 1410 pounds of food was ordered. Find the total number of adults in the group and the total number of children in the group

Answer 1

A + c = 148 -> c = 148 - a
12a + 9c = 1410

12a + 9(148 - a) = 1410
12a + 1332 - 9a = 1410
3a = 78
a = 26

26 + c = 148
c = 122

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Answer 2

We'll call the number of adults (x). Since there are 148 people total, the number of children will be 148 minus the number of adults, or (148 - x). 

12 pounds for each adult = 12x 
9 pounds for each child = 9 (148-x) = (1332 - 9x) 

The total pounds for adults plus children is 1,410, so the equation would be: 

12x + (1332 - 9x) = 1410 

Combine like terms: 

3x + 1332 = 1410 

Get x term alone by subtracting 1332 from both sides: 

3x = 78 

Solve for x by dividing both sides by 3 

x = 26 = number of adults