Alexis found 2 times as many shells as Tina. Tina found 5 more shells than Phillip. Together Alexis and Phillip found 16 shells. How many di

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Alexis found 2 times as many shells as Tina. Tina found 5 more shells than Phillip. Together Alexis and Phillip found 16 shells. How many did each person find?

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    2021-09-20T22:39:10+00:00

    Answer:

    • Phillip: 2 shells
    • Tina: 7 shells
    • Alexis: 14 shells

    Step-by-step explanation:

    The problem statement gives rise to three equations in three unknowns. Let a, t, p represent the numbers of shells found by Alexis, Tina, and Phillip, respectively. Then the equations are …

    … a = 2t . . . . . . . Alexis found 2 times as many as Tina

    … t = 5 +p . . . . . Tina found 5 more than Phillip

    … a + p = 16 . . . . Alexis and Phillip together found 16 shells

    These equations can be solved a variety of ways. For example, we can use substitution to get two equations in t and p.

    … t – p = 5 . . . . . rearrange the second equation

    … 2t +p = 16 . . . substitute for a in the third equation

    Adding these gives …

    … 3t = 21

    t = 7

    Then

    a = 2t = 2·7 = 14

    p = 16 – a = 16 – 14 = 2

    Alexis found 14 shells, Tina found 7 shells, Phillip found 2 shells.

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