Joel made egg sandwiches and tuna sandwiches in the ratio 2:3. He then made 15 more tuna sandwiches and the ratio changed to 1:3. How many sandwiches did Joel make in all show your work and explain how u found your answer.

40 sandwiches

Step-by-step explanation:

egg sandwiches : tuna sandwiches

2 : 3

Multiply by x because we do not know how many sandwiches, just the ratio

2x : 3x

Add 15 tuna sandwiches

2x : 3x+15

Now the ratio is 1:3

egg sandwiches : tuna sandwiches

1 : 3

Multiply by y because we do not know how many sandwiches, just the ratio

y : 3y

Set the number of egg sandwiches equal

2x = y

then set the number of tuna sandwiches equal

3x+15 = 3y

We know have a system of 2 equations and 2 unknowns

Substitute y = 2x into the second equation

3x+15 = 3 (2x)

Distribute

3x+15 = 6x

Subtract 3x from each side

3x-3x+15 = 6x-3x

15 = 3x

Divide by 3

15/3 = 3x/3

5 = x

egg sandwiches : tuna sandwiches

2 : 3

Multiply by x because we do not know how many sandwiches, just the ratio

2x : 3x

2*5 3*5

10 15

He originally made 10 egg sandwiches and 15 tuna sandwiches

Then he made 15 more tuna sandwiches

The total number of sandwiches he made is

10+15+15 = 40 sandwiches