Respuesta :

tramserran

Answer: 40

Step-by-step explanation:

Let x represent the original ratio and y represent the final ratio:

  Egg  :     Tuna

  2x            3x

                    +15     15 tuna were added

  2x = y       3x + 15 = 3y     y and 3y are the final 1:3 ratio

Now you have a system of equations. I am going to choose the substitution method. "2x" can be substituted for "y" in the second equation:

3x + 15 = 3y

3x + 15 = 3(2x)

3x + 15 = 6x

        15 = 3x

         5 = x

Egg (final): 2x  = 2(5)   = 10

Tuna (final): 3x + 15   = 3(5) + 15   = 15 + 15   = 30

Egg (final) + Tuna (final) = Total sandwiches

      10       +        30        =         40

e = number of egg sandwiches

t = number of tuna sandwiches

since they're on a ratio of 2:3 then e/t = 2/3


[tex]\bf e:t\qquad 2:3\qquad \cfrac{e}{t}=\cfrac{2}{3}\implies e=\cfrac{2t}{3}~\hfill \stackrel{\textit{then he made 15 more tuna ones}}{\cfrac{e}{t+15}~~=~~\cfrac{1}{3}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{doing some substitution for \underline{e}}}{\cfrac{~~\frac{2t}{3}~~}{t+15}=\cfrac{1}{3}}\implies \left( \cfrac{2t}{3} \right)3=(t+15)1\implies 2t=t+15 \\\\\\ \boxed{t=15}~\hspace{7em}e=\cfrac{2(15)}{3}\implies \boxed{e=10}~\hfill \boxed{\stackrel{total~e+t+15}{40}}[/tex]

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