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A shop sells milkshakes in two sizes. The small milkshake is 300 ml and the large milkshake is 2/3 more than the small milkshake. Find the size of the large milkshake.

Mathematics

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Answers

5 parts
a

M38000\text{M}38000

b

M56243.20\text{M}56243.20

c(i)

500 ml500 \text{ ml}

d
15

Step-by-step solution

11 steps

Part a· 2 steps

  1. Calculate the loss amount.

    Loss is 5% of M40 000.

    Loss=0.05×40000=M2000\text{Loss} = 0.05 \times 40000 = \text{M}2000
  2. Calculate the selling price.

    Selling price is the original price minus the loss.

    Selling Price=40000−2000=M38000\text{Selling Price} = 40000 - 2000 = \text{M}38000

    The selling price is M38000\boxed{\text{M}38000}.

Part b

M56243.20\text{M}56243.20

  1. Use the compound interest formula to find the value after three years.

    The formula for compound interest is A=P(1+r)nA = P(1 + r)^n, where AA is the final amount, PP is the principal amount, rr is the annual interest rate, and nn is the number of years.
    Given P=M50000P = \text{M}50000, r=4%=0.04r = 4\% = 0.04, and n=3n = 3 years.

    A=50000(1+0.04)3A = 50000(1 + 0.04)^3
  2. Calculate the final value.

    A=50000(1.04)3A = 50000(1.04)^3 A=50000×1.124864A = 50000 \times 1.124864 A=M56243.20A = \text{M}56243.20

    The price of the land after three years is M56243.20\boxed{\text{M}56243.20}.

Part c(i)

500 ml500 \text{ ml}

  1. Calculate the amount by which the large milkshake is bigger.

    The large milkshake is 23\frac{2}{3} more than the small milkshake.

    Increase=23×300 ml=200 ml\text{Increase} = \frac{2}{3} \times 300 \text{ ml} = 200 \text{ ml}
  2. Find the size of the large milkshake.

    Large milkshake=Small milkshake+Increase\text{Large milkshake} = \text{Small milkshake} + \text{Increase} Large milkshake=300 ml+200 ml=500 ml\text{Large milkshake} = 300 \text{ ml} + 200 \text{ ml} = 500 \text{ ml}

    The size of the large milkshake is 500 ml\boxed{500 \text{ ml}}.

Part c(ii)3:5

  1. Express the ratio of the small milkshake to the large milkshake.

    Small milkshake : Large milkshake = 300 ml : 500 ml

  2. Simplify the ratio.

    Divide both sides by 100.

    300:500=3:5300 : 500 = 3 : 5

    The ratio in its simplest form is 3:5\boxed{3:5}.

Part d15

  1. Calculate the total simple interest earned.

    The formula for simple interest is I=A−PI = A - P, where II is the interest, AA is the final amount, and PP is the principal.
    Given A=M17400A = \text{M}17400 and P=M12000P = \text{M}12000.

    I=17400−12000=M5400I = 17400 - 12000 = \text{M}5400
  2. Use the simple interest formula to find the rate rr.

    The formula for simple interest is I=PRT100I = \frac{PRT}{100}, where PP is the principal, RR is the rate, and TT is the time in years.
    Given I=M5400I = \text{M}5400, P=M12000P = \text{M}12000, and T=3T = 3 years.

    5400=12000×r×31005400 = \frac{12000 \times r \times 3}{100}
  3. Solve for rr.

    5400=120×r×35400 = 120 \times r \times 3 5400=360r5400 = 360r r=5400360r = \frac{5400}{360} r=15r = 15

    The value of rr is 15\boxed{15}.

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