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21 September, 22:17

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.

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  1. 21 September, 22:37
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    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    He originally made 10 egg sandwiches and 15 tuna sandwiches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
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