Molly took part in a math quiz and scored 55 points on 30 questions. Of the questions, there were 3-point word problems, 2-point calculation

Question

Molly took part in a math quiz and scored 55 points on 30 questions. Of the questions, there were 3-point word problems, 2-point calculation questions, and 1-point multiple-choice questions. She answered 5 more 2-point questions than 1-point questions correctly. Find how many of each type of question she answered correctly.

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Thành Đạt 3 years 2021-08-27T08:12:46+00:00 1 Answers 5 views 0

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    2021-08-27T08:14:38+00:00

    Answer:

    3\ point\ word = 5

    2\ point\ word = 15

    1\ point\ word = 10

    Step-by-step explanation:

    Given

    Represent

    3-point word with T;

    2-point with U and

    1-point with V

    U = 5 + V — (1)

    If total questions is 30, then

    T + U + V = 30 — (2)

    If total points is 55, then

    3T + 2U + V = 55 — (3)

    Substitute 5 + V for U in (2) and (3)

    T + U + V = 30 — (2)

    T + 5 + V + V = 30

    T + 5 + 2V = 30

    T + 2V = 25 —- (4)

    3T + 2U + V = 55 — (3)

    3T + 2(5 + V) + V = 55

    3T + 10 + 2V + V = 55

    3T + 10 + 3V = 55

    3T  + 3V = 55 - 10

    3T  + 3V = 45

    Divide through by 3

    T + V = 15 —- (5)

    Subtract (5) from (4)

    (T + 2V = 25 )- (T + V = 15)

    T - T + 2V - V = 25 - 15

    V = 10

    Recall that:

    U = 5 + V

    U = 5 + 10

    U = 15

    Substitute 10 for V in (5)

    T + V = 15

    T + 10 = 15

    T = 5

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