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Question
Each of the consultants at Firm L is to receive a year-end bonus this year. Bianca will receive a larger bonus than any other consultant, but only dollars more than David will receive. None of the consultants will receive a smaller bonus than David. If the total amount of money to be distributed in bonuses at Firm L this year is dollars, what is the largest bonus Bianca can receive?
Answer Choices
- A.
- B.
- C.
- D.
- E.
Steps
| Explanation | Calculations | Help |
|---|---|---|
We name the bonus for Bianca as B and the bonus for David as D. | Theory & Tactics Method Card TRANS1-A Click to view full details | |
We translate "only 400 dollars more than David will receive" into an equation. | Theory & Tactics Method Card TRANS1-C Click to view full details | |
We interpret "None of the consultants will receive a smaller bonus than David", so to make Bianca's bonus as large as possible, we assign each of the other 23 consultants exactly D. | Theory & Tactics Method Card TRANS4-B Click to view full details | |
We translate "total amount of money to be distributed in bonuses at Firm L this year is 90,000 dollars" into an equation for all bonuses. | Theory & Tactics Method Card TRANS1-C Click to view full details | |
We substitute the expression for B into the total and simplify to isolate D. | Theory & Tactics Method Card EQUA1-B Click to view full details | |
We subtract 400 from both sides and divide by 25 to find D. | Theory & Tactics Method Card EQUA1-C Click to view full details | |
We add 400 to David's bonus to find Bianca's bonus. |
Scroll horizontally to view all columns
Final Answer
C
Question
Each of the consultants at Firm L is to receive a year-end bonus this year. Bianca will receive a larger bonus than any other consultant, but only dollars more than David will receive. None of the consultants will receive a smaller bonus than David. If the total amount of money to be distributed in bonuses at Firm L this year is dollars, what is the largest bonus Bianca can receive?
Answer Choices
- A.
- B.
- C.
- D.
- E.
Steps
| Explanation | Calculations | Help |
|---|---|---|
We name the bonus for Bianca as B and the bonus for David as D. | Theory & Tactics Method Card TRANS1-A Click to view full details | |
We translate "only 400 dollars more than David will receive" into an equation. | Theory & Tactics Method Card TRANS1-C Click to view full details | |
We interpret "None of the consultants will receive a smaller bonus than David", so to make Bianca's bonus as large as possible, we assign each of the other 23 consultants exactly D. | Theory & Tactics Method Card TRANS4-B Click to view full details | |
We translate "total amount of money to be distributed in bonuses at Firm L this year is 90,000 dollars" into an equation for all bonuses. | Theory & Tactics Method Card TRANS1-C Click to view full details | |
We substitute the expression for B into the total and simplify to isolate D. | Theory & Tactics Method Card EQUA1-B Click to view full details | |
We subtract 400 from both sides and divide by 25 to find D. | Theory & Tactics Method Card EQUA1-C Click to view full details | |
We add 400 to David's bonus to find Bianca's bonus. |
Scroll horizontally to view all columns
Final Answer
C