Question

Justine and Roy both ordered takeout dinners for their family. Justine paid $15 for three sodas and three burgers. Roy paid $12 for four sodas and two burgers. Equations representing this situation are given below, where x represents the cost of a soda and y represents the cost of a burger. Find out how much it costs to purchase 1 hamburger and 1 soda.

3x+3y=15
4x+2y=12

Answer 1

The cost of 1 soda is : x = $ 1

The cost of 1 hamburger is : y = $4

Explanation:

Here, the given set of equations is:

3 x + 3 y = 15 ........ (1)

4 x + 2 y = 12 ...... (2)

Here, x represents the cost of a soda.

and y represents the cost of a burger.

Now, solving the given system of equation by ELIMINATION METHOD.

Multiply (1) with 4 and (2) with -3 , we get:

12 x + 12 y = 60 ........ (a)

-12 x - 6 y = - 36 ...... (b)

Adding both equations,we get:

12 x + 12 y -12 x - 6 y = - 36 + 60

or, 6 y = 24

or, y = 34/6 = 4

or, y = 4

Putting the value of y = 4 in (1) , w e get:

3 x + 3 y = 15 ⇒ 3 x + 3 (4) = 15

or, 3 x = 15 - 12 = 3

or, x = 3/ 3 = 1, or x = 1

Hence, here, the cost of 1 soda is : x = $ 1

And the cost of 1 hamburger is : y = $4