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1.1.3 The budget of R6 144 will be spent equally on 6 items: food, drinks, entertainment, decorations, transportation and gifts. Calculate, using the long division method, how much will each item get.

Mathematics

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Step-by-step solution

9 steps

Part 1.1· 4 steps

Quants balons s'ajusten a la paret?

  1. Convert dimensions to cm (same units as balloon width).

    Longitud: 2 m=200 cm2\,\mathrm{m} = 200\,\mathrm{cm}
    Alçada: 1.5 m=150 cm1.5\,\mathrm{m} = 150\,\mathrm{cm}
    Ample baló: 30 cm30\,\mathrm{cm}

  2. Balons al llarg de la longitud (divisió llarga)

    30\longdiv200−18020\begin{array}{r|r} & 30\longdiv{200}\\ - & 180\\ \hline & 20 \end{array}

    30×6=180 cm30 \times 6 = 180\,\mathrm{cm}
    200−180=20 cm200 - 180 = 20\,\mathrm{cm} (resta)
    ∴6\therefore 6 balons al llarg.

  3. Balons al llarg de l'alçada (divisió llarga)

    30\longdiv150−1500\begin{array}{r|r} & 30\longdiv{150}\\ - & 150\\ \hline & 0 \end{array}

    30×5=150 cm30 \times 5 = 150\,\mathrm{cm}
    150−150=0 cm150 - 150 = 0\,\mathrm{cm}
    ∴5\therefore 5 balons d'alçada.

  4. Total balons

    6×5=306 \times 5 = 30 balons.

    30 balons

Part 1.2· 1 step

Pressupost de la festa (cost baló 0.20 \euro0.20\,\mathrm{\euro})

  1. Cost total

    30×0.20=6 \euro30 \times 0.20 = 6\,\mathrm{\euro}

    6,\euro

Part 1.3· 4 steps

Àrees (paret, espai en l'aire, globus)

  1. Àrea paret

    2 m×1.5 m=3 m22\,\mathrm{m} \times 1.5\,\mathrm{m} = 3\,\mathrm{m}^2

  2. Diàmetre baló 30 cm=0.3 m30\,\mathrm{cm} = 0.3\,\mathrm{m}, radi r=0.15 m=320 mr = 0.15\,\mathrm{m} = \frac{3}{20}\,\mathrm{m}

    Àrea 1 baló:

    πr2=π(320)2=π⋅9400=9π400 m2\pi r^2 = \pi \left(\frac{3}{20}\right)^2 = \pi \cdot \frac{9}{400} = \frac{9\pi}{400}\,\mathrm{m}^2
  3. Àrea total globus

    30×9π400=270π400=27π40 m230 \times \frac{9\pi}{400} = \frac{270\pi}{400} = \frac{27\pi}{40}\,\mathrm{m}^2
  4. Espai en l'aire (descobert)

    3−27π40 m23 - \frac{27\pi}{40}\,\mathrm{m}^2

    \boxed{Àrea paret: 3 m23\,\mathrm{m}^{2}
    Àrea globus: 27π40 m2\dfrac{27\pi}{40}\,\mathrm{m}^{2}
    Espai aire: 3−27π40 m23 - \dfrac{27\pi}{40}\,\mathrm{m}^{2}}

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