Answer:the number of hot dogs is 10
Step-by-step explanation:
Let x represent the number of hamburgers.
Let y represent the number of hot dogs.
The ratio of hamburgers to hot dogs is 6 to 5. This means that the ratio of x to y is 6/5
x/y = 6/5
5x = 6y
x = 6y/5
Three times the number of hot dogs is 6 more than twice the number of hamburgers. This means that
3y = 2x + 6 - - - - - - - - -1
Substituting x = 6y/5 into equation 1, it becomes
3y = 2(6y/5) + 6
3y = 12y/5 + 6
Multiplying both sides of the equation by 5, it becomes
15y = 12y + 30
15y - 12y = 30
3y = 30
y = 30/3 = 10
x = 6y/5 = 6×10/5
x = 60/5 = 12
Substitute on equation 2, y = -4x + 7. so equation 1 becomes 2x - (-4x + 7) = 6x - 7 = 5. 6x = 12, so x = 2. from above, y = -4x+7 = -4(2) + 7 = -1
