53) If an investment account lost 12% of its value and is currently worth $15,00

Question

53) If an investment account lost 12% of its value and is currently worth $15,000, what was it worth before the loss? Write and solve an appropriate equation 54)An online retailer is selling used books for $4.99, and you have $54 to spend. Write an equation to express the situation and solve t to find out how many books you can buy ifyou must pay 8.5% tax and an additional 12% of the total purchase price (with tax), for shipping 55) Suppose you want to treat your colleagues to lattes at a local coffee shop. The drinks are $3.75 cach, plus you plan to buy a S2.50 scone for yourself. You also tip the barista l 5% and have to pay g 75% sales tax. How many lattes can you afford if you have $64 to spend? Write an equation to express the situation and can buy solve it to find out how many lattes you

Explanation / Answer

53). Let the value of the investment before the loss be $ x. After 12 % loss, the current value of the investment is 0.88x so that0.88x = 15000. Hence x = 15000/0.88 = $ 17045.45( on rounding off to the nearest cent). Thus, the value of the investment before the loss was $ 17045.45.

54). Let x be the number of books that can be bought. The the price of x number of books is 4.99x. After paying 8.5 % tax, the cost of the books becomes 4.99x(1 +0.085)= 5.41415x. Further, after paying 12 % shipping charges, the total cost increases to 5.41415x( 1+0.12) = 6.063848 x. Hence, 6.063848 x 54 so that x 54/6.063848 or, x 8.905236411. Since x has to be a whole number, therefore, 8 used books can be purchased.

55). The information given seems to be insufficient. Hence we will assume that:

1. The number of colleagues(including the host) is a.

2. The prices of scone and latte is same.

Suppose x number of lattes can be consumed. The price of drinks is 3.75a. The price of lattes is 2.50x. Then the price of drinks and the lattes is 3.75a+2.50x. The payment to the barista is 15 % of 3.75a+2.50x or, 0.5625 a +0.375x. Further, 8.75 % sales tax amounts to 8.75 % of 3.75a+2.50x or, 0.328125 a + 0.21875x. Then, 3.75a+2.50x +0.5625 a +0.375x + 0.328125 a + 0.21875x 64 or, 4.640625 a + 3.09375 x 64 or, 3.09375x (64-4.640625 a) so that x (64-4.640625a)/ 3.09375.

Now, if a ( whole number) is known, x can be determined. x is a whole number, lower than or equal to (64-4.640625a)/ 3.09375.

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