Question
an office manager has $10,000 to spend on new equipment. He planned to purchase 300 lamps for $72 each he completed the calculation and concluded that there would be plenty of money left to buy additional equipment
300×72 equals
300×7+300×2 equals
2100 +600 equals 2700. Does the office manager conclusion makes sense explain your answer.
300×72 equals
300×7+300×2 equals
2100 +600 equals 2700. Does the office manager conclusion makes sense explain your answer.
Answers
GPT-4o mini
Let's analyze the calculations step by step:
1. The office manager is planning to purchase 300 lamps, with each lamp costing $72.
2. The total cost for the lamps can be calculated as follows:
\[
300 \text{ lamps} \times 72 \text{ dollars/lamp} = 21,600 \text{ dollars}
\]
However, there seems to be a mistake in the office manager’s breakdown of the multiplication, as they are calculating \(300 \times 72\) in parts:
- They broke it down as \(300 \times 7 + 300 \times 2\), which is:
\[
300 \times 7 = 2100
\]
\[
300 \times 2 = 600
\]
- Adding those two results gives:
\[
2100 + 600 = 2700
\]
3. The office manager’s calculation of \(2700\) is incorrect for the total cost of 300 lamps at $72 each; it should actually be $21,600.
4. Since the office manager has a total budget of $10,000, purchasing 300 lamps at a total cost of $21,600 would exceed the budget significantly.
**Conclusion:**
The office manager's conclusion that there would be plenty of money left for additional equipment is incorrect. In fact, if he spends $21,600 on lamps, he will significantly exceed his budget of $10,000, leaving him with a deficit of $11,600. Therefore, the office manager needs to reassess the number of lamps he can afford within his budget.
1. The office manager is planning to purchase 300 lamps, with each lamp costing $72.
2. The total cost for the lamps can be calculated as follows:
\[
300 \text{ lamps} \times 72 \text{ dollars/lamp} = 21,600 \text{ dollars}
\]
However, there seems to be a mistake in the office manager’s breakdown of the multiplication, as they are calculating \(300 \times 72\) in parts:
- They broke it down as \(300 \times 7 + 300 \times 2\), which is:
\[
300 \times 7 = 2100
\]
\[
300 \times 2 = 600
\]
- Adding those two results gives:
\[
2100 + 600 = 2700
\]
3. The office manager’s calculation of \(2700\) is incorrect for the total cost of 300 lamps at $72 each; it should actually be $21,600.
4. Since the office manager has a total budget of $10,000, purchasing 300 lamps at a total cost of $21,600 would exceed the budget significantly.
**Conclusion:**
The office manager's conclusion that there would be plenty of money left for additional equipment is incorrect. In fact, if he spends $21,600 on lamps, he will significantly exceed his budget of $10,000, leaving him with a deficit of $11,600. Therefore, the office manager needs to reassess the number of lamps he can afford within his budget.