a group of students go out for lunch. if two have hamburgers and five have hotdogs, the bill will be $8.00. if five have hamburgers and two have hotdogs,the bill will be $9.50. what is the price of a hamburger?
1.50
what is the hotgogs price
To find the price of a hamburger, let's assign some variables:
Let's assume the price of a hamburger is 'x' dollars, and the price of a hotdog is 'y' dollars.
From the given information, we can form two equations:
Equation 1: 2x + 5y = 8.00
Equation 2: 5x + 2y = 9.50
We can now solve this system of equations to find the values of 'x' and 'y' using the method of substitution or elimination.
Let's use the method of substitution:
From Equation 1, we can solve for 'x' in terms of 'y':
2x = 8.00 - 5y
x = (8.00 - 5y) / 2
Substitute this value of 'x' into Equation 2:
5((8.00 - 5y)/2) + 2y = 9.50
Now we can solve the equation for 'y'. Multiply through by 2 to eliminate the fraction:
5(8.00 - 5y) + 4y = 19.00
40.00 - 25y + 4y = 19.00
Combine like terms:
-21y = -21.00
Divide both sides by -21 to solve for 'y':
y = 1.00
Now that we have the value of 'y', substitute it back into Equation 1 to solve for 'x':
2x + 5(1.00) = 8.00
2x + 5 = 8.00
2x = 3.00
x = 1.50
Therefore, the price of a hamburger is $1.50.
b = price of burgers
d = price of dogs
2b + 5d = 8.00
5b + 2d = 9.50
Solve simultaneously