(1 3/4) divided by (1/5) =
(7/4) ÷ (1/5) =
7/4 multiplied by 5/1 =
35/4 or 8 3/4 <===
To solve this problem, you'll want to substitute the first equation into the second or the other way around. The equations given are: 1. 3 paperback books + 5 hardcover books = $80.10; 2. 7 paperback books + 4 hardcover books = $100.65. It is helpful to rearrange the first equation to find 5 hardcover books = $80.10 - 3 paperback books, leading to hardcover book = $16.02 - 0.6 paperback books. Now, substitute this into the second equation: 7 paperback books + 4 ($16.02 - 0.6 paperback books) = $100.65, which simplifies to 7 paperback books + $64.08 - 2.4 paperback books = $100.65. This results in 4.6 paperback books = $100.65 - $64.08 = $36.57, thus paperback book = $7.95. You can then use this price in the first equation to determine the hardcover book price: 3 paperback books + 5 hardcover books = $80.10, substituting gives 3($7.95) + 5 hardcover books = $80.10, which leads to 5 hardcover books = $80.10 - $23.85 = $56.25, therefore hardcover book = $11.25. Hence, the total cost for one paperback and one hardcover book is $7.95 + $11.25 = $19.20.
Determining the answer here is quite straightforward. Ella has a total of $2.16, and we need to ascertain the cost per piece of gum.
It is known that if the gum cost one cent less, she would have acquired three more pieces.
Currently, with 8 pieces priced at 27 cents each, a reduced price would allow her to have 8.64 pieces. This outcome, even after rounding, is incorrect as it does not yield 11.
For 9 pieces at 24 cents each, a cheaper price would mean she could have 9.39 pieces, which still does not round to 12, indicating it's incorrect.
At 16 pieces costing 13.5 cents each, at one cent less, she would acquire 17.28 pieces, which also confirms it's wrong because rounding does not yield 19.
When purchasing 24 pieces at 9 cents each, with the cheaper price, she could buy 27 pieces, which is valid since 27-24 equals 3.
Therefore, the correct answer is D) 24
