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Solve for x and calculate the lengths of the sides of the triangle, width of the rectangle, and Juzi and Leo's money.

Mathematics

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Step-by-step solution

11 steps
+2x+5+ 2x + 5 40=4x−540 = 4x - 5
  1. Solve for xx.

    40+5=4x40 + 5 = 4x 45=4x45 = 4x x=454x = \frac{45}{4} x=11.25x = 11.25
  2. Calculate the length of each side.

    Side 1: x−5=11.25−5=6.25 cmx - 5 = 11.25 - 5 = 6.25 \text{ cm}
    Side 2: x−5=11.25−5=6.25 cmx - 5 = 11.25 - 5 = 6.25 \text{ cm}
    Side 3: 2x+5=2(11.25)+5=22.5+5=27.5 cm2x + 5 = 2(11.25) + 5 = 22.5 + 5 = 27.5 \text{ cm}
    The lengths of the sides of the triangle are 6.25 cm, 6.25 cm, and 27.5 cm\boxed{\text{6.25 cm, 6.25 cm, and 27.5 cm}}.

    B.

  3. Let the width of the rectangle be ww.

  4. The length ll is twice the width, so l=2wl = 2w.

  5. The perimeter PP of a rectangle is given by P=2(l+w)P = 2(l + w).

    Substitute the given perimeter and expressions for length and width:

    48=2(2w+w)48 = 2(2w + w) 48=2(3w)48 = 2(3w) 48=6w48 = 6w
  6. Solve for ww.

    w=486w = \frac{48}{6} w=8w = 8

    The width of the rectangle is 8 cm\boxed{\text{8 cm}}.

    C.

  7. Let Juzi's money be yy.

  8. Leo has twice as much as Juzi, so Leo has $2y$.

  9. Their total sum of money is 750.

    y+2y=750y + 2y = 750 3y=7503y = 750
  10. Solve for yy.

    y=7503y = \frac{750}{3} y=250y = 250
  11. Calculate how much Leo has.

    Leo has 2y=2×250=5002y = 2 \times 250 = 500.
    Leo has sh. 500\boxed{\text{sh. 500}}.

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