Answer:
Hence There are 26 adults and 122 child at summer camp.
They can stay for maximum 1 day at summer camp.
Step-by-step explanation:
Given:
Let the number of adults be 'x'.
Also Let the number of child be 'y'
Total Number of people = 148
Now Total Number of people is equal to sum of number of adults and number of child.
framing in equation form we get;
[tex]x+y=148 \ \ \ \ \ equation \ 1[/tex]
Also Given:
Amount of food ordered for each adult = 12 pounds
Amount of food ordered for each child = 9 pounds
Total amount of food = 1410 pounds
Now we know that;
Total amount of food is equal to Amount of food ordered for each adult multiplied by number of adults plus Amount of food ordered for each child multiplied by number of child.
framing in equation form we get;
[tex]12x+9y =1410 \ \ \ \ equation\ 2[/tex]
No Multiplying equation 1 by 9 we get;
[tex]9(x+y)=148\times9\\\\9x+9y=1332 \ \ \ \ equation\ 3[/tex]
Now Subtracting equation 3 from equation 2 we get;
[tex](12x+9y)-(9x-9y) =1410-1332\\\\12x+9y-9x-9y = 78\\\\3x=78\\\\x= \frac{78}{3} =26[/tex]
Now Substituting the value of x in equation 1 we get;
[tex]x+y=148\\\\26+y=148\\\\y=148-26=122[/tex]
Hence There are 26 adults and 122 child at summer camp.
Now Food ordered for each child = 9 pound.
Number of child = 122
Total Amount of food for child = [tex]9\times 122 =1098\ pounds[/tex]
Now Food ordered for each adult = 12 pound.
Number of adults = 26
Total Amount of food for adults = [tex]12\times 26 =312\ pounds[/tex]
Total amount of food ordered = 1410 pounds
Total amount of food required each day for both adults and child = 1098+312 =1410 pounds
Number of days will be equal to Total amount of food ordered divided Total amount of food required each day for both adults and child.
framing in equation form we get;
Number of days = [tex]\frac{1410}{1410} =1[/tex]
Hence they can stay for maximum 1 days at summer camp.
