2 hamburgers and a fry cost 3 dollars. 2 fries and a hamburger costs 2.50 dollars. Find the value of 3 hamburgers and a fry.

Question

Do systems of equations.

Answer 1

To determine the value of 3 hamburgers and 1 fry, we must first determine the value of 1 hamburger and 1 fry.

Lets first define the following variables:

H = the value of 1 hamburger

F = the value of 1 fry

Given that 2 hamburgers and a fry cost 3 dollars, and 2 fries and a hamburger costs 2.50 dollars, we can write the following two equations:

2H + F = 3 (Equation 1)

2F + H = 2.5 (Equation 2)

Now, we want to be able to substitute one equation into the other so let’s rearrange Equation 1 to isolate the variable F:

2H + F = 3 (Equation 1)

F = 3 - 2H By subtracting both sides by 2H

Next, substitute this new equation into Equation 2 above:

2F + H = 2.5 (Equation 2)

2(3 - 2H) + H = 2.5 By plugging in 3 - 2H into F in Equation 2

Now we have an equation with just one variable (H). Let’s solve for H:

6 - 4H + H = 2.5 By distributing the 2 into (3 - 2H)

6 - 3H = 2.5 By combining -4H + H

-3H = -3.5 By subtracting 6 from both sides

H = 3.5/3 or 7/6 By dividing both sides by -3

Now that we know H = 7/6, we can plug this into our equation for F from above to get the value of F:

F = 3 - 2H

F = 3 - 2(7/6) By plugging in 7/6 for H

F = 3 - 7/3 By multiplying 2 times 7/6

F = 9/3 - 7/3 By changing 3 to 9/3 so it has the same denominator as 7/3

F = 2/3 By subtracting fractions

Finally, we have the values of F and H, so we can solve for the value of 3 hamburgers and 1 fry, or:

3H + F

3(7/6) + 2/3

21/6 + 4/6

25/6 or $4.17

Therefore the value of 3 hamburgers and 1 fry is $4.17.

Answer 2

Consider H the cost of one hamburger and F the cost of one fry.

Then we have:

2H + F =3 equation (1)

2F + H = 2.5 equation (2)

From (2) we have 2F + H = 2.5

-2F = -2F

____________

H = 2.5 - 2F equation (3)

Replacing H from (3) at equation (1) we have:

2(2.5 - 2F) + F = 3

5-4F + F = 3

5-3 = 3F

F= 2 /3

Replacing F in equation (3) we have:

H = 2.5 - 2 (2/3)

H = 2.5 - 4/3. = (7.5 - 4)/3 = 3.5 / 3 =7/6

Now aswering the question, the price of 3 hamburgers and a free is 3H + F .

3 (7/6) + 2/3 = 21/6 + 2/3 = 21/6 + 4/6 = 25/6 = 4.17

Answer 3

https://www.youtube.com/watch?v=SD3kGiFeOFM

See the video.

Answer 4

Let H = the cost of one Hamburger, and let F = the cost of one bag of fries.

Then we can write 2 equations from the given facts:

2H + F = $3.00

H + 2F = $2.50

For the sake of simplicity, let's dispense with the currency notation and just use unitless numbers, and multipy the second equation by 2:

2H + 4F = 5

If we subtract the first equation from this last equation, we arrive at:

3F = 2

So F = 2/3.

Since 2H + F = 3,

2H + (2/3) = 3.

If we multiply both sides by 3,

6H + 2 = 9

6H = 7

and H = 7/6.

Therefore,

3H + F = 3(7/6) + (2/3) = (21/6) + (4/6)

= (25/6) = 4 1/6

In currency notation,

3 hamburgers and a bag of fries cost $4.17

By the way, Desmos can be used to solve the equations and verify the results.