Question 1061800
let x = number of boys
let y = number of girls.


since each boy ate 5 hot dogs and each girls ate 3 hot dogs and the total number of hot dogs eaten were 51, you get:


5x + 3y = 51


since each boy drank 7 sodas and each girl drank 4 sodas and the total number of sodas that were drunk was 70, you get:


7x + 4y = 70


these are two equations that need to be solved simultaneously.


once solved, you will get x = 6 and y = 7.


i solved using elimination.


i started with:


5x + 3y = 51
7x + 4y = 70


i multiplied both sides of the first equation by 7 and multiplied both sides of the second equation by 5 to get:


35x + 21y = 357
35x + 20y = 350


i then subtracted the second equation from the first equation to get:


y = 7


i then replaced y with 7 in the first original equation to get:


5x + 21 = 51


i then solved for x to get x = 6.


you can confirm the solution is good by replacing x with 6 and y with 7 in both equations to see that both equations are true.


i did, and they are, so i can assume the solution is good.