A restaurant sells slices for $2 and calzones for $3. On Monday, a total of 54 slices and calzones were sold, and the cashier collected a total of $120 from sales of slices and calzones. Let x represent the number of slices and y represent the number of calzones. Which system of equations represents the situation?

The system of equations is:

x  +  y  =  54

2*x  +  3*y  =  120

And the solution is   x  =  42     y  =  12

Step-by-step explanation:

x number of slices and

y number of calzones

On Monday they collected 120 $

Then    2*x  + 3* y  = 120

And the total of 54 slices and calzones were sold, then

x  +  y  =  54

The system is:

x  +  y  =  54

2*x  +  3*y  =  120

Solving for x and y

y  =  54 - x

2*x  +  3* ( 54  -  x  )  = 120

2*x  +  162  -  3*x   =  120     ⇒    - x  =  - 42

x  =  42

And  

y =  54  -  42   ⇒  y  =  12

{xx+1.5y==54−y60

The total number of slices and calzones sold is 54. This gives the equation x+y=54. Solve the equation for x to obtain x=54−y. The total cost of the slices plus the total cost of the calzones gives the total value, $120. The equation representing this situation is 2y+3x=120. Dividing both sides by 2 gives x+1.5y=60.

7

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2

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