New Home Forums AMC 8 AMC 8, 2019, Problem Marathon

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  • #99586
    Arisha Roy
    Participant

    Problem 21

    What is the area of the triangle formed by the lines \(y=5, y=1+x\), and \(y=1-x\) ?

    #99587
    Arisha Roy
    Participant

    Solution:

    3 equations will be,

    \(y=5.........(i)\)

    \(y=1+x........(ii)\)

    \(y=1-x ..........(iii)\)

    By solving eq(i) and eq(ii) we get, \(y=5, x=4\).

    By solving eq(i) and eq(iii) we get, \(y=5, x=-4\).

    By solving eq(ii) and eq(iii) we get, \(y=1, x=0\).

    We will get a triangle base and height of which will be 8 and 4.

    Area will be \(\frac{4 \times 8}{2}=16\)

    #99685
    Arisha Roy
    Participant

    Problem 22

    A store increased the original price of a shirt by a certain percent and then lowered the new price by the same amount. Given that the resulting price was \(84 \%\) of the original price, by what percent was the price increased and decreased?

    #99687
    Arisha Roy
    Participant

    Solution

    Let the original price is \(x\) and price is increased by \(y%\).

    So, \( x \times \frac{100+y}{100} \times \frac{100-y}{100}=x \times \frac{84}{100}\)

    \(10000-y^2=8400\)

    \(y=40\)

    By \(40\) percent was the price increased and decreased.

    • This reply was modified 1 year, 4 months ago by Arisha Roy.
    #99971
    Arisha Roy
    Participant

    Problem 23

    After Euclid High School's last basketball game, it was determined that \(\frac{1}{4}\) of the team's points were scored by Alexa and \(\frac{2}{7}\) were scored by Brittany. Chelsea scored 15 points. None of the other 7 team members scored more than 2 points. What was the total number of points scored by the other 7 team members?

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