Vong grilled 21 burgers at a block party. He grilled the same number of pounds of turkey burgers as hamburgers. Each turkey burger weighed 1/4 pound and each hamburger weighed 1/3 pound. How many of each did Vong grill?

How does it equal 12 and 9

t+b = 21 - counting burgers

1/4 t = 1/3 b - weighing burgers

t=12
b=9

To find the number of turkey burgers and hamburgers Vong grilled, we can set up an equation. Let's denote the number of turkey burgers as 'T' and the number of hamburgers as 'H'.

According to the given information, Vong grilled a total of 21 burgers:

T + H = 21 (Equation 1)

We also know that the weight of each turkey burger is 1/4 pound and the weight of each hamburger is 1/3 pound. Since Vong grilled the same number of pounds of turkey burgers as hamburgers, we can set up another equation based on the weights:

(1/4)T = (1/3)H (Equation 2)

To solve this system of equations, we can use substitution or elimination.

Let's rearrange Equation 2 to express T in terms of H:

T = (4/3)H (Equation 3)

Substitute Equation 3 into Equation 1:

(4/3)H + H = 21

Multiply through by 3 to eliminate the fraction:

4H + 3H = 63

Combine like terms:

7H = 63

Divide both sides by 7:

H = 9

Now, substitute the value of H back into Equation 3 to find T:

T = (4/3) * 9 = 12

Therefore, Vong grilled 12 turkey burgers and 9 hamburgers.