Question

A school has $15,000 to spend on computer monitors. The school plans to purchase 200 monitors for $89 each. A teacher completes the calculations below and concludes that the school has enough money to buy the monitors. 200×89===(200×8)+(200×9)1,600+1,8003,400 Which explains whether or not the teacher's conclusion is correct? (1 point) Responses The teacher did not use the Distributive Property correctly. 200×89=(200+8)×(200+9)=208×209=43,472 The total cost of the monitors is $43,472, which is more than $15,000. So, the teacher's conclusion is not correct. The teacher did not use the Distributive Property correctly. 200 × 89 = ( 200 + 8 ) × ( 200 + 9 ) = 208 × 209 = 43 , 472 The total cost of the monitors is $43,472, which is more than $15,000. So, the teacher's conclusion is not correct. The teacher did not use the Distributive Property correctly. 200×89=(200×89)+(1×89)=17,800+89=17,889 The total cost of the monitors is $17,889, which is more than $15,000. So, the teacher's conclusion is not correct. The teacher did not use the Distributive Property correctly. 200 × 89 = ( 200 × 89 ) + ( 1 × 89 ) = 17 , 800 + 89 = 17 , 889 The total cost of the monitors is $17,889, which is more than $15,000. So, the teacher's conclusion is not correct. The teacher did not use the Distributive Property correctly. 200×89=(200×80)+(200×9)=16,000+1,800=17,800 The total cost of the monitors is $17,800, which is more than $15,000. So, the teacher's conclusion is not correct. The teacher did not use the Distributive Property correctly. 200 × 89 = ( 200 × 80 ) + ( 200 × 9 ) = 16 , 000 + 1 , 800 = 17 , 800 The total cost of the monitors is $17,800, which is more than $15,000. So, the teacher's conclusion is not correct. The teacher used the Distributive Property correctly to show that the total cost of the computers is $3,400, which is less than $15,000. So, the teacher's conclusion is correct. The teacher used the Distributive Property correctly to show that the total cost of the computers is $3,400, which is less than $15,000. So, the teacher's conclusion is correct.

Answer 1

The teacher's conclusion is not correct.

Let's break down the calculations properly.

To find the total cost for 200 monitors at $89 each, we can calculate:

\[
200 \times 89 = 17800
\]

Now, let's analyze the teacher's use of the Distributive Property. The teacher incorrectly calculated \(200 \times 89\) using wrong factors. The teacher attempted to use:

\[
(200 + 8) \times (200 + 9) = 208 \times 209
\]

But this multiplication method does not correctly apply to the situation at hand.

Let’s calculate \(208 \times 209\):

\[
208 \times 209 = 43,472
\]

This indicates a total cost much greater than what was needed, indicating a misunderstanding of the application of the property.

In the correct approach using the proper values, the total cost of the monitors is actually:

\[
200 \times 89 = 17800
\]

Since \(17,800\) is indeed more than \(15,000\), we can conclude that:

The correct response is: **The teacher did not use the Distributive Property correctly. The total cost of the monitors is $17,800, which is more than $15,000. So, the teacher's conclusion is not correct.**