Numbers, Fractions, Decimals, and Percents

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These are the solutions to the WASSCE past questions on the topic: Numbers, Fractions, Decimals, and Percents.
When applicable, the TI-84 Plus CE calculator (also applicable to TI-84 Plus calculator) solutions are provided for some questions.
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Percent Applications

$ \underline{\text{Change and Percent of Change}} \\[3ex] (1.)\:\: change = new - initial \\[5ex] (2.)\:\: \%\;\;of\;\;change = \dfrac{change}{initial} * 100 \\[5ex] (3.)\;\; \text{If A is p% more than B, then A = (100 + p)% of B} \\[3ex] (4.)\;\; \text{If A is p% less than B, then A = (100 – p)% of B} \\[5ex] \underline{\text{Percent:Proportion}} \\[3ex] (5.)\;\; \dfrac{is}{of} = \dfrac{\%}{100} \\[5ex] (6.)\;\;\underline{\text{Percent:Equation}} \\[3ex] is \rightarrow equal\;\;to \\[3ex] of\;\; \rightarrow multiply \\[3ex] what \;\; \rightarrow variable \\[5ex] \underline{\text{Wholesale and Retail}} \\[3ex] (7.)\:\: \text{Sale Price } = \text{Initial Price } - \text{Discount} \\[5ex] (8.)\:\: \%\;Discount = \dfrac{Discount}{\text{Initial Price}} * 100 \\[5ex] (9.)\;\; \text{Profit } = \text{Selling Price } - \text{Cost Price} \\[3ex] (10.)\;\; \%\;Profit = \dfrac{Profit}{\text{Cost Price}} * 100 \\[5ex] (11.)\;\; \text{Loss } = \text{Cost Price } - \text{Selling Price} \\[3ex] (12.)\;\; \%\;Loss = \dfrac{Loss}{\text{Cost Price}} * 100 $

(5.) A man left an estate for his wife, extended family and children; Dakorah, Gifty and Gemma.
In the will, $\dfrac{1}{3}$ of the estate must be given to Dakorah, $\dfrac{1}{3}$ of the remaining to Gifty, $\dfrac{3}{4}$ of what still remains to Gemma, $\dfrac{2}{3}$ of the remaining to the wife and the rest to the extended family.
If the wife received a total of GH¢ 105,500.00 as her share of the estate, find the:
(a.) total value of the estate;
(b.) extended family's share of the estate.

$ \text{Let the amount of the estate} = e \\[3ex] "of" \text{ in the context of the question means } "multiply" \\[5ex] \underline{\text{Dakorah}} \\[3ex] \dfrac{1}{3} * e = \dfrac{e}{3} \\[5ex] Remaining = e - \dfrac{e}{3} = \dfrac{3e}{3} - \dfrac{e}{3} = \dfrac{2e}{3} \\[5ex] \underline{\text{Gifty}} \\[3ex] \dfrac{1}{3} * \dfrac{2e}{3} = \dfrac{2e}{9} \\[5ex] Remaining = \dfrac{2e}{3} - \dfrac{2e}{9} = \dfrac{6e}{9} - \dfrac{2e}{9} = \dfrac{4e}{9} \\[5ex] \underline{\text{Gemma}} \\[3ex] \dfrac{3}{4} * \dfrac{4e}{9} = \dfrac{e}{3} \\[5ex] Remaining = \dfrac{4e}{9} - \dfrac{e}{3} = \dfrac{4e}{9} - \dfrac{3e}{9} = \dfrac{e}{9} \\[5ex] \underline{\text{Wife}} \\[3ex] \dfrac{2}{3} * \dfrac{e}{9} = \dfrac{2e}{27} \\[5ex] Remaining = \dfrac{e}{9} - \dfrac{2e}{27} = \dfrac{3e}{27} - \dfrac{2e}{27} = \dfrac{e}{27} \\[5ex] \underline{\text{Extended Family}} \\[3ex] \dfrac{e}{27} \\[5ex] (a.) \\[3ex] \dfrac{2e}{27} = 105500 \\[5ex] 2e = 105500(27) \\[3ex] e = \dfrac{105500(27)}{2} \\[5ex] e = GH¢\;1424250.00 \\[5ex] (b.) \\[3ex] \dfrac{e}{27} \\[5ex] = \dfrac{1424250}{27} \\[5ex] = GH¢\;52750.00 \\[3ex] $ Student: Mr. C, is there a way we can check the solution to this question?
Teacher: We can...
Find the sum of all those fractions
It should be equal to e
Student: Can we do it?
Teacher: Sure, let's do it.

$ \underline{\text{Dakorah + Gifty + Gemma + Wife + Extended Family}} \\[3ex] \dfrac{e}{3} + \dfrac{2e}{9} + \dfrac{e}{3} + \dfrac{2e}{27} + \dfrac{e}{27} \\[5ex] = e $

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