At a concession stand seven hot dogs and four hamburgers cost 14.00 dollars. Four hot dogs and seven hamburgers cost 16.25.
find the cost of one hot dog and one hamburger.
Timed please hurry.
7d + 4h = 1400
4d + 7h = 1625
use elimination,
multiply the first by 7 and the second by 4, the subtract. The h's will drop out
I am sure you can handle it.
lol no this was no help :)
To find the cost of one hot dog and one hamburger, we can set up a system of equations based on the given information.
Let's assume the cost of one hot dog is represented by 'h' and the cost of one hamburger is represented by 'b'.
From the first equation, we know that 7h + 4b = 14.00 (equation 1).
From the second equation, we know that 4h + 7b = 16.25 (equation 2).
To solve this system of equations, we can use either substitution or elimination method. Let's use the substitution method:
Step 1: Solve equation 1 for h:
7h + 4b = 14
7h = 14 - 4b
h = (14 - 4b) / 7 (equation 3)
Step 2: Substitute equation 3 into equation 2 and solve for b:
4(14 - 4b) / 7 + 7b = 16.25
(56 - 16b) / 7 + 7b = 16.25
56 - 16b + 49b = 16.25 * 7
56 + 33b - 16b = 113.75
17b = 113.75 - 56
17b = 57.75
b = 57.75 / 17
b ≈ 3.39
Step 3: Substitute the value of b back into equation 3 to find the value of h:
h = (14 - 4(3.39)) / 7
h = (14 - 13.56) / 7
h ≈ 0.06
Therefore, the cost of one hot dog is approximately $0.06 and the cost of one hamburger is approximately $3.39.
To find the cost of one hot dog and one hamburger, let's assign variables to the unknowns. Let's say the cost of one hot dog is "x" dollars and the cost of one hamburger is "y" dollars.
From the given information, we can create two equations:
Equation 1: 7x + 4y = 14.00
(Seven hot dogs and four hamburgers cost $14.00)
Equation 2: 4x + 7y = 16.25
(Four hot dogs and seven hamburgers cost $16.25)
To solve this system of equations, we can use the method of substitution.
Step 1: Solve Equation 1 for x in terms of y
Rearrange Equation 1:
7x = 14 - 4y
Divide both sides by 7:
x = (14 - 4y)/7
Step 2: Substitute x in Equation 2 with (14 - 4y)/7
4((14 - 4y)/7) + 7y = 16.25
Step 3: Simplify Equation 2
(56 - 16y)/7 + 7y = 16.25
Multiply both sides by 7 to eliminate the fraction:
56 - 16y + 49y = 113.75
Combine like terms:
33y = 57.75
Divide both sides by 33:
y = 1.75
Step 4: Substitute y = 1.75 back into Equation 1 to find x
x = (14 - 4(1.75))/7
x = 6.50/7
x ≈ 0.93
Therefore, the cost of one hot dog is approximately $0.93 and the cost of one hamburger is $1.75.