Meaghan goes to the grocery store to buy hot dogs and hamburgers for a cookout. She buys a total of 16 packages for a total of $75.16. If a package of hot dogs costs $2.65 and a package of hamburgers costs $6.29, determine how many packs of each she bought.
a = # hot dogs, b = # hamburgers
a + b = 16
2.65a + 6.29b = 75.16
Solve using substitution/elimination and arrive at a = 7, b = 9, indicating 7 hot dogs and 9 hamburgers.
number of hamburger packs --- x
number of hot dog packs ---- 16-x
6.29x + 2.65(16-x) = 75.16
times 100 and expand
629x + 265(16-x) = 7516
629x + 4240 - 265x = 7516
364x = 3276
x = 9
So 9 packs of hamburgers and 7 packs of hotdogs.
Meghan goes to the grocery store to buy hot dogs and hamburgers for a cookout. she buys total of 6 packages for a total of $30.46. if a package of hot dogs costs $2.65 and a package of hamburgers cost $6.29, determine how many packs of each she bought
To solve this problem, let's first set up a system of equations.
Let's use the variable x to represent the number of packages of hot dogs Meaghan bought, and the variable y to represent the number of packages of hamburgers she bought.
From the given information, we know that the total number of packages Meaghan bought is 16. Therefore, we can write the equation:
x + y = 16 --- Equation 1
We also know that the total cost of all the packages is $75.16. Since a package of hot dogs costs $2.65 and a package of hamburgers costs $6.29, we can write the equation:
2.65x + 6.29y = 75.16 --- Equation 2
Now we have a system of equations:
x + y = 16 --- Equation 1
2.65x + 6.29y = 75.16 --- Equation 2
To find the values of x and y, we can solve this system of equations.
Let's solve it using the substitution method.
From Equation 1, we can solve for x in terms of y:
x = 16 - y
Substitute this value of x into Equation 2:
2.65(16 - y) + 6.29y = 75.16
Now we can solve for y:
42.4 - 2.65y + 6.29y = 75.16
Combine like terms:
3.64y = 32.76
Divide both sides by 3.64:
y = 32.76 / 3.64
y ≈ 9
Now substitute this value of y back into Equation 1 to find the value of x:
x + 9 = 16
x = 16 - 9
x = 7
Therefore, Meaghan bought 7 packages of hot dogs and 9 packages of hamburgers.