Question

The ratio of hamburgers to hot dogs is 6 to 5. Three times the number of hot dogs is 6 more than twice the number of hamburgers. How many hot dogs are there?

Answer 1

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