SOLUTION: Every boy had 5 hot dogs and 7 sodas. Every girl had 3 hot dogs and 4 sodas. Together, the children ate 51 hot dogs and 70 sodas. How many children were there?

Question 1061800: Every boy had 5 hot dogs and 7 sodas. Every girl had 3 hot dogs and 4 sodas. Together, the children ate 51 hot dogs and 70 sodas. How many children were there?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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