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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?

Respuesta :

Answer:

42 slices and 12 calzones

Step-by-step explanation:

Let x represent the number of slices

Let y represent the number of calzones

We can set up a system of equations to solve this problem

x + y = 54     (54 total slices and calzones were sold)

2x + 3y = 120         (the cost and the number of each that were sold)

Solve the first equation for either variable...

y = 54 - x

Now plug that value into the second equation...

2x + 3(54 - x) = 120       now solve for x

2x + 162 - 3x = 120

     -x = -42

          x = 42

If 42 slices were sold, then there were

42 + y = 54

 

      y = 12   calzones sold

jcultr4s3nse
We could represent this problem with the equations 3s+2c=120 and c+s=54.

We can use 1 equation to solve the other in this type of problem.
Subtract s on both sides on the second equation so we end up with c=54-s. Then, we can substitute that in place of c for the original equation.
3s+2(54-s)=120
Now we only have 1 variable, and the problem is solvable.
3s+108-2s=120
S+108=120
S=12
Now, insert 12 into the original equation to find out the value of c.
C=54-12
C=42
Don’t forget to check!
3(12)+2(42)=129
36+84=120
120=120
C=42 and s=12
Hope this helps!

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