Krystal grilled 21 burgers at a block party. She grilled the same number of pounds of turkey burgers as hamburgers. Each turkey burger weighed 1/4 pounds and each hamburger weighed 1/3 pound. How many of each did Krystal grill?
~Please help me and provide an explanation for your answer.
Please and thank you!
number of hamburgers ---- x
number of turkeyburgs --- 21-x
weight of hamburgers = (1/3)x
weight of turkeyburgs = (1/4)(21-x
so (1/3)x = (1/4)(21-x)
times 12 , the LCD
4x = 3(21-x)
4x = 63-3x
7x = 63
x = 9
so 9 hamburgers and 12 turkeyb's
To solve this problem, let's start by assigning variables to represent the unknowns.
Let's say x represents the number of turkey burgers that Krystal grilled, and y represents the number of hamburgers.
According to the given information, each turkey burger weighs 1/4 pound, and each hamburger weighs 1/3 pound.
Since Krystal grilled a total of 21 burgers, we can form an equation based on the number of burgers: x + y = 21.
Additionally, we know that the weight of the turkey burgers equals the weight of the hamburgers: (1/4)x = (1/3)y.
To eliminate the fractions, we can multiply both sides of the second equation by 12 (the least common multiple of 4 and 3), which gives us:
3x = 4y.
Now, we have a system of two equations:
x + y = 21,
3x = 4y.
We can solve this system using various methods, but let's use the substitution method:
From the first equation, we can express x in terms of y:
x = 21 - y.
Substituting this value of x into the second equation:
3(21 - y) = 4y.
Distributing 3 to both terms:
63 - 3y = 4y.
Bringing like terms to one side:
63 = 7y + 3y,
63 = 7y,
y = 9.
Now that we have the value of y, we can substitute it back into x + y = 21 to find x:
x + 9 = 21,
x = 21 - 9,
x = 12.
Therefore, Krystal grilled 12 turkey burgers and 9 hamburgers.