Numbers, Fractions, Decimals, and Percents
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These are the solutions to the CSEC past questions on Numbers, Fractions, Decimals, and Percents.
The TI-84 Plus CE shall be used for applicable questions.
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For calculations involving scientific notation as applicable, change the mode to SCI.
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 $
Formula Sheet: List of Formulae
(i.) $\dfrac{2}{3} \;\;of\;\; \left(\dfrac{1}{8} + \dfrac{5}{12} \div \dfrac{1}{9}\right)$, giving your answer in EXACT form.
(ii.) $314.2 - \dfrac{26082}{52164}$, giving your answer in standard form.
(b.) Jim packed several cases of fruit juice for sale.
Each case contained 24 boxes of juice in 3 different varieties: apple, orange, and pineapple in the ratio 2:5:1 respectively.
(i.) How many boxes of pineapple juice were packed in each case?
(ii.) The profit gained from selling ALL of the boxes of pineapple juice is $35.64.
Each box of pineapple juice was sold at $3.34.
(a.) Show that the cost price of a box of pineapple juice is $2.35
(b.) Calculate the percentage profit made on the sale of the boxes of pineapple juice.
$ (a.) (i.) \\[3ex] \dfrac{2}{3} \;\;of\;\; \left(\dfrac{1}{8} + \dfrac{5}{12} \div \dfrac{1}{9}\right) \\[5ex] \underline{PEMDAS} \\[3ex] \text{Parenthesis: Division and Addition} \\[3ex] Division: \\[3ex] \dfrac{5}{12} \div \dfrac{1}{9} \\[5ex] = \dfrac{5}{12} * \dfrac{9}{1} \\[5ex] = \dfrac{15}{4} \\[5ex] Addition: \\[3ex] \dfrac{1}{8} + \dfrac{15}{4} \\[5ex] = \dfrac{1}{8} + \dfrac{30}{8} \\[5ex] = \dfrac{31}{8} \\[5ex] of \implies Multiplication: \\[3ex] \dfrac{2}{3} \;\;of\;\; \dfrac{31}{8} \\[5ex] = \dfrac{2}{3} * \dfrac{31}{8} \\[5ex] = \dfrac{31}{12} \\[5ex] (ii.) \\[3ex] 314.2 - \dfrac{26082}{52164} \\[5ex] = 314.2 - 0.5 \\[3ex] = 313.7 \\[3ex] = 3.137 * 10^{2}...\text{in standard form} \\[5ex] (b.)(i.) \\[3ex] \text{24 boxes containing 3 fruit varieties} \\[3ex] \text{Apple : Orange : Pineapple = 2 : 5 : 1} \\[3ex] \text{sum of ratios} = 2 + 5 + 1 = 8 \\[3ex] \text{number of boxes of pineapple juice} = \dfrac{1}{8} * 24 \\[5ex] = 3\;boxes \\[3ex] $ (ii.) (a.)
Selling Price, of each pineapple juice box = $3.34
Profit gained from selling all pineapple juice boxes = $35.64
But we are not given the number of pineapple juice boxes that were sold
To show that the cost price of a pineapple juice box = $2.35, we shall assume that 36 boxes of pineapple juice boxes were sold.
$ \underline{\text{36 boxes of pineapple juice}} \\[3ex] \text{Selling Price} = 3.34(36) = \$120.24 \\[3ex] Profit = \$35.64 \\[3ex] Profit = \text{Selling Price} - \text{Cost Price} \\[3ex] \text{Cost Price} = \text{Selling Price} - Profit \\[3ex] = 120.24 - 35.64 \\[3ex] = \$84.60 \\[3ex] \underline{\text{1 box of pineapple juice}} \\[3ex] C.P = \dfrac{84.60}{36} = \$2.35 \\[5ex] (b.) \\[3ex] \text{%Profit} = \dfrac{\text{Profit}}{\text{Cost Price}} * 100 \\[5ex] = \dfrac{35.64}{84.6} * 100 \\[5ex] = 42.12765957\% \\[3ex] \approx 42.1\%...\text{to 3 significant figures} $
(1.)(a.)(i.)
(ii.)
