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Sample Question 9:
Step 1: First, find out how many widgets Janabel makes on Day 20. You can write a linear equation \(y=-1+2x\) to represent this situation.
Step 2: Plug in 20 for \(x\) in the equation: \(y=-1+2(20)\)
Step 3: Simplify that to \(y=-1+40\), which simplifies further to \(y=39\).
Step 4: Now, find the sum of the sequence from 1, 3, 5, up to 39. This can be obtained by taking the average of the first and last term, and then multiplying by the total number of terms. The equation is \(\frac{(1 + 39)(20)}{2}\).
Step 5: Perform the calculation to find that the total number of widgets Janabel sold in 20 days is 400. Therefore the answer is \(\textbf{(D)}~400\).
On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working \(20\) days?
\(\textbf{(A) }39\qquad\textbf{(B) }40\qquad\textbf{(C) }210\qquad\textbf{(D) }400\qquad \textbf{(E) }401\)
Answer Keys
Question 9: DSolutions
Question 9Step 1: First, find out how many widgets Janabel makes on Day 20. You can write a linear equation \(y=-1+2x\) to represent this situation.
Step 2: Plug in 20 for \(x\) in the equation: \(y=-1+2(20)\)
Step 3: Simplify that to \(y=-1+40\), which simplifies further to \(y=39\).
Step 4: Now, find the sum of the sequence from 1, 3, 5, up to 39. This can be obtained by taking the average of the first and last term, and then multiplying by the total number of terms. The equation is \(\frac{(1 + 39)(20)}{2}\).
Step 5: Perform the calculation to find that the total number of widgets Janabel sold in 20 days is 400. Therefore the answer is \(\textbf{(D)}~400\).