High School

1. The total mass of Ali, John, and Thomas is 173 kg. Thomas is 21 kg heavier than Ali. Ali is 8 kg lighter than John. Find Thomas' mass.

2. Mr. Gopal bought 4 identical T-shirts and a belt. The belt cost 3 times as much as each T-shirt. If the belt cost $30 more than a T-shirt, how much did Mr. Gopal spend altogether?

Answer :

Let's solve these problems step-by-step.

  1. Finding Thomas' mass:

    We are given the following information:

    • The total mass of Ali, John, and Thomas is 173 kg.
    • Thomas is 21 kg heavier than Ali.
    • Ali is 8 kg lighter than John.

    Let:

    • [tex]A[/tex] be Ali's mass
    • [tex]J[/tex] be John's mass
    • [tex]T[/tex] be Thomas' mass

    From the information:

    • [tex]T = A + 21[/tex]
    • [tex]A = J - 8[/tex]
    • [tex]A + J + T = 173[/tex]

    Substitute [tex]T = A + 21[/tex] and [tex]A = J - 8[/tex] into the equation:

    [tex]A + J + (A + 21) = 173[/tex]

    Simplify this:

    [tex]2A + J + 21 = 173[/tex]

    Rearrange to solve for [tex]J[/tex]:

    [tex]2A + J = 152[/tex]

    Substitute [tex]A = J - 8[/tex] into this equation:

    [tex]2(J - 8) + J = 152[/tex]

    Simplify:

    [tex]2J - 16 + J = 152[/tex]

    [tex]3J - 16 = 152[/tex]

    [tex]3J = 168[/tex]

    [tex]J = 56 \text{ kg}[/tex]

    Now, substituting [tex]J = 56[/tex] back to find [tex]A[/tex]:

    [tex]A = J - 8 = 56 - 8 = 48 \text{ kg}[/tex]

    Finally, calculate [tex]T[/tex]:

    [tex]T = A + 21 = 48 + 21 = 69 \text{ kg}[/tex]

    So, Thomas' mass is 69 kg.

  2. Finding how much Mr. Gopal spent:

    We are given that:

    • The cost of the belt is 3 times the cost of a T-shirt.
    • The belt costs $30 more than a T-shirt.

    Let:

    • [tex]x[/tex] be the cost of one T-shirt.
    • Therefore, the cost of the belt is [tex]3x[/tex].

    From the given information:

    [tex]3x = x + 30[/tex]

    Solve for [tex]x[/tex]:

    [tex]3x - x = 30[/tex]

    [tex]2x = 30[/tex]

    [tex]x = 15[/tex]

    So, each T-shirt costs $15.

    Calculate the cost of the belt:

    [tex]3x = 3(15) = 45[/tex]

    So, each belt costs $45.

    Total spending by Mr. Gopal is:

    [tex]4x + 3x = 4(15) + 45 = 60 + 45 = 105[/tex]

    Mr. Gopal spent a total of $105.

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