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If the chairs cost US$700, find their cost in Kenya shillings.

Mathematics

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2 parts
a

Ug.sh.25,200,000\text{Ug.sh.25,200,000}

b

K.sh.60,000\text{K.sh.60,000}

Step-by-step solution

4 steps

Here are the solutions to the problems.

o) Given that: 24p=102four24_p = 102_{\text{four}}. Find the base pp.

Step 1: Convert the number 24p24_p from base pp to base 10.

24p=(2×p1)+(4×p0)24_p = (2 \times p^1) + (4 \times p^0) 24p=2p+424_p = 2p + 4

Step 2: Convert the number 102four102_{\text{four}} from base 4 to base 10.

102four=(1×42)+(0×41)+(2×40)102_{\text{four}} = (1 \times 4^2) + (0 \times 4^1) + (2 \times 4^0) 102four=(1×16)+(0×4)+(2×1)102_{\text{four}} = (1 \times 16) + (0 \times 4) + (2 \times 1) 102four=16+0+2102_{\text{four}} = 16 + 0 + 2 102four=18102_{\text{four}} = 18

Step 3: Equate the base 10 values and solve for pp.

2p+4=182p + 4 = 18 2p=18−42p = 18 - 4 2p=142p = 14 p=142p = \frac{14}{2} p=7p = 7

The base pp must be greater than the largest digit used in 24p24_p, which is 4. Since p=7p=7, this is a valid base.

The base pp is 7\boxed{7}.

26. The table below shows how a bank buys and sells foreign currencies. Study and use it to answer the questions that follow.

CurrencyBuying in Ug.shSelling in Ug.sh
1 US dollar (US$)Ug.sh.3600Ug.sh.3700
1 Pound sterling (£)Ug.sh.4650Ug.sh.4700
1 Kenya shillings (K.sh)Ug.sh.40Ug.sh.42

Part a· 2 steps

Ssebidde came back to Uganda from USA and constructed a house which cost him $7000. Find the equivalent cost of the house in Uganda shillings.

  1. Determine the correct exchange rate.

    Ssebidde has US dollars and wants to convert them to Uganda shillings. This means the bank is buying US dollars from Ssebidde.
    From the table, the bank's buying rate for 1 US dollar is Ug.sh.3600.

  2. Calculate the cost in Uganda shillings.

    Cost in Ug.sh=Amount in US$×Buying rate for US$\text{Cost in Ug.sh} = \text{Amount in US\$} \times \text{Buying rate for US\$}

    Cost in Ug.sh=7000×3600\text{Cost in Ug.sh} = 7000 \times 3600 Cost in Ug.sh=25,200,000\text{Cost in Ug.sh} = 25,200,000

    The equivalent cost of the house in Uganda shillings is Ug.sh.25,200,000\boxed{\text{Ug.sh.25,200,000}}.

Part b

K.sh.60,000\text{K.sh.60,000}

If the chairs cost US$700, find their cost in Kenya shillings.

  1. Convert US$700 to Uganda shillings.

    To find the equivalent value, we first convert the US dollars to Uganda shillings. Assuming a person has US700 and wants to convert it to Uganda shillings, the bank **buys** US dollars from them. Rate: 1 US\ = Ug.sh.3600 (Buying rate for US$)

    Amount in Ug.sh=700×3600\text{Amount in Ug.sh} = 700 \times 3600 Amount in Ug.sh=2,520,000\text{Amount in Ug.sh} = 2,520,000

  2. Convert the Uganda shillings amount to Kenya shillings.

    Now, to find the equivalent value in Kenya shillings, we convert the Uganda shillings to Kenya shillings. If a person has Uganda shillings and wants Kenya shillings, the bank sells Kenya shillings to them.
    Rate: 1 Kenya shilling = Ug.sh.42 (Selling rate for K.sh)

    Amount in K.sh=Amount in Ug.shSelling rate for K.sh\text{Amount in K.sh} = \frac{\text{Amount in Ug.sh}}{\text{Selling rate for K.sh}} Amount in K.sh=2,520,00042\text{Amount in K.sh} = \frac{2,520,000}{42} Amount in K.sh=60,000\text{Amount in K.sh} = 60,000

    The cost of the chairs in Kenya shillings is K.sh.60,000\boxed{\text{K.sh.60,000}}.

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