Solve 12.50x + 25x ≤ 150 for x.

Question

Responses:

x ≤ 4

x 10

x ≤ 10

x ≥ 4

Answer 1

To solve the inequality \(12.50x + 25x \leq 150\), we first combine like terms on the left side:

\[ 12.50x + 25x = 37.50x \]

So the inequality becomes:

\[ 37.50x \leq 150 \]

Next, we divide both sides by 37.50 to isolate \(x\):

\[ x \leq \frac{150}{37.50} \]

Now, we perform the division:

\[ \frac{150}{37.50} = 4 \]

Thus, we can rewrite the inequality as:

\[ x \leq 4 \]

The correct response is:

x ≤ 4

Answer 2

Sheila plans to buy as many shirts as she can. The inequality for this would be 18.75x ≤ 150. How can Sheila determine if 9 is a solution to this inequality
Responses:

Sheila can add 9 and 18.75. She would get 27.75. Since this is less than 150, 9 is a solution.

Sheila can subtract 150 and 18.75. She would get 131.25. Since this is less than 150, 9 is a solution.

Sheila can substitute 9 into the equation for x. 18.75 times 9 is 168.75. Since this number is not less than 150, 9 is not a solution.

Sheila can substitute 9 into the equation for x. 18.75 divided by 9 is 2.08. Since this is less than 150, 9 is a solution.

Answer 3

To determine if \(9\) is a solution to the inequality \(18.75x \leq 150\), we substitute \(9\) for \(x\) in the inequality and check if it holds true.

1. Substitute \(x = 9\) into the inequality: \[ 18.75 \times 9 \]

2. Calculate \(18.75 \times 9\): \[ 18.75 \times 9 = 168.75 \]

3. Now we check if \(168.75 \leq 150\):

   • This is not true because \(168.75\) is greater than \(150\).

Thus, \(9\) is not a solution to the inequality \(18.75x \leq 150\).

The correct response is:

Sheila can substitute 9 into the equation for x. 18.75 times 9 is 168.75. Since this number is not less than 150, 9 is not a solution.

Answer 4

Sheila is doing some shopping online before the holidays. She received a $150 gift card for her birthday and wants to buy some items from the table below.

Sheila plans on buying matching sets of scarfs and hats. Using the table, can you write an inequality statement (do not solve!) that shows how many sets she can buy with her gift card? Use x as your unknown.

Shirt=18.75
Jacket= 37.50
scarf= 12.50
Hat= 25.00
Responses:
18.75x + 37.50y = 150

12.50x + 25y = 150

12.50x + 25x ≤ 150

12.50x + 25x ≥ 150

Answer 5

To represent Sheila's plan to buy matching sets of scarves and hats using her $150 gift card, we need to express the total cost of the items in terms of \(x\), where \(x\) represents the number of sets of scarves and hats she plans to buy.

From the table, we know:

• Each scarf costs $12.50.
• Each hat costs $25.00.

Since Sheila is buying matching sets, we can represent the cost for \(x\) sets of scarves and hats as follows:

• The cost of \(x\) scarves is \(12.50x\).
• The cost of \(x\) hats is \(25x\).

Combining these, the total cost for \(x\) sets is: \[ 12.50x + 25x \]

Now, since she wants to ensure that she does not exceed her gift card amount of $150, we can set up the inequality: \[ 12.50x + 25x \leq 150 \]

Thus, the correct inequality statement is:

12.50x + 25x ≤ 150