QQuestionMathematics
QuestionMathematics
"Becky is offered the two deals below:
Deal 1: She will get a quarter on the first day of the week. Each day thereafter for one week, she will receive double what she received on the previous day.
Deal 2: She will get $4 each day for 1 week.
Which statement is true in every aspect regarding these two deals?
A. She should go with deal 1 because mc^026 - 1.jpg is greater than mc^026 - 2.jpg by $3.75.
B. She should go with deal 1 because mc^026 - 3.jpg is greater than mc^026 - 4.jpg by $35.50.
C. She should go with deal 2 because mc^026 - 5.jpg is greater than mc^026 - 6.jpg by $27.33.
D. She should go with deal 2 because mc^026 - 7.jpg is greater than mc^026 - 8.jpg by $48.50."
10 months agoReport content
Answer
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Step 1:: Calculate the total amount Becky would receive from Deal 1.
S_{7} = \frac{1}{4} \frac{1-2^{7}}{1-2} = 122
There are 7 terms in total. We can calculate the sum of this geometric series using the formula: So, for Deal 1: Plugging these values into the formula:
Step 2:: Calculate the total amount Becky would receive from Deal 2.
T_{2} = 4 imes 7 = $ 28
Deal 2 offers $4 each day for a week, and there are 7 days in a week. So,
Step 3:: Compare the total amounts for each deal.
- Total amount from Deal 2: $28$
From Step 1 and Step 2, we have:
Step 4:: Find the difference between the total amounts for each deal.
Difference = Total_{Deal1} - Total_{Deal2} = 122 - 28 = $ 94
Since $94 is greater than any of the dollar amounts mentioned in the options, none of the given options is correct. However, if we are to compare the deals in terms of the total amount received, Becky should definitely choose Deal 1.
Final Answer
Becky should choose Deal 1 because it offers a greater total amount of money: $122, which is $94 more than the total amount offered by Deal 2.
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