6 burgers and 3 hot dogs cost $27. 5 burgers and one hot dog cost $18.75. what is the price of a hot dog? what is the price of a hamburger?
first, represent unknowns using variables:
let x = price of hamburger
let y = price of hotdogs
set up equation:
(1) 6x + 3y = 27
(2) 5x + y = 18.75
there are several ways to solve this,, but id we use substitution method,,
choose an equation (in this case, equation (2)),, then express one of the variables in terms of the other,, thus if we express y in terms of x:
5x + y = 18.75
y = 18.75 - 5x
then we substitute this to equation (1):
6x + 3y = 27
6x + 3(18.75 - 5x) = 27
now simplify this and solve for x. after that substitute this x to either equations to get y.
To find the price of a hot dog and a hamburger, let's assign variables:
Let's assume the price of a hamburger is "x" dollars.
Let's assume the price of a hot dog is "y" dollars.
Based on the given information, we can set up two equations:
Equation 1: 6x + 3y = 27 (6 burgers and 3 hot dogs cost $27)
Equation 2: 5x + y = 18.75 (5 burgers and 1 hot dog cost $18.75)
To solve this system of equations, we can use substitution or elimination method.
Let's use the elimination method to solve:
Multiply Equation 2 by 3 to make the coefficients of "y" in both equations equal:
(3) * (5x + y) = (3) * (18.75)
15x + 3y = 56.25
Now, subtract Equation 1 from the new equation:
(15x + 3y) - (6x + 3y) = 56.25 - 27
15x - 6x + 3y - 3y = 29.25
Combine like terms:
9x = 29.25
Divide both sides by 9:
x = 3.25
The price of a hamburger is $3.25.
Now, substitute the value of x into either original equation (let's use Equation 1):
6x + 3y = 27
6(3.25) + 3y = 27
19.5 + 3y = 27
3y = 27 - 19.5
3y = 7.5
Divide both sides by 3:
y = 2.5
The price of a hot dog is $2.50.