Match each scenario with the equation that can be used to solve it.

Question

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Darius is 38 years old. In 4 years he will be 3 times as old as Gia. How old is Gia?
I think of a number, multiply it by 3 and then add four to get 42. What number am I thinking of?
Lucia goes to the art store and spends $38. She buys a canvas for $20 and some new paints. If each paint cost $3, how many did she buy?
Chelsea owes her mom $38. She starts paying her mom back $4 per week. After some weeks, she realizes she only owes her mom $2 more. How many weeks has she been paying her mom back?
A rectangle has a length of 4 units and a width of x + 3 units. If the area is 42, what is the value of x?
3x + 4 = 42
4x + 2 = 38
3 (x + 4) = 42
3x + 20 = 38
4 (x + 3) = 42

Answer 1

Here are the matched scenarios with their corresponding equations:

1. Darius is 38 years old. In 4 years he will be 3 times as old as Gia. How old is Gia?

   • Equation: 3(x + 4) = 42 (Let x be Gia's current age)

2. I think of a number, multiply it by 3 and then add four to get 42. What number am I thinking of?

   • Equation: 3x + 4 = 42

3. Lucia goes to the art store and spends $38. She buys a canvas for $20 and some new paints. If each paint costs $3, how many did she buy?

   • Equation: 3x + 20 = 38 (Let x be the number of paints)

4. Chelsea owes her mom $38. She starts paying her mom back $4 per week. After some weeks, she realizes she only owes her mom $2 more. How many weeks has she been paying her mom back?

   • Equation: 4x + 2 = 38 (Let x be the number of weeks)

5. A rectangle has a length of 4 units and a width of x + 3 units. If the area is 42, what is the value of x?

   • Equation: 4(x + 3) = 42

So, here are the matches neatly summarized:

• 1 → 3(x + 4) = 42
• 2 → 3x + 4 = 42
• 3 → 3x + 20 = 38
• 4 → 4x + 2 = 38
• 5 → 4(x + 3) = 42

Answer 2

Solve each equation. Match the solution with the correct equation. Some answer choices may be unneeded.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
2x - 6 = 24
2x + 6 = 24
2(x + 6) = 24
2(x - 6) = 24

9
6
18
15

Answer 3

Here are the solutions to each equation and their corresponding matches:

1. Equation: \(2x - 6 = 24\)
   Solution:
   \(2x = 24 + 6\)
   \(2x = 30\)
   \(x = 15\)

2. Equation: \(2x + 6 = 24\)
   Solution:
   \(2x = 24 - 6\)
   \(2x = 18\)
   \(x = 9\)

3. Equation: \(2(x + 6) = 24\)
   Solution:
   \(x + 6 = 24 / 2\)
   \(x + 6 = 12\)
   \(x = 12 - 6\)
   \(x = 6\)

4. Equation: \(2(x - 6) = 24\)
   Solution:
   \(x - 6 = 24 / 2\)
   \(x - 6 = 12\)
   \(x = 12 + 6\)
   \(x = 18\)

Now, matching the solutions:

• For \(2x - 6 = 24\) → Solution: 15
• For \(2x + 6 = 24\) → Solution: 9
• For \(2(x + 6) = 24\) → Solution: 6
• For \(2(x - 6) = 24\) → Solution: 18

So the matches are as follows:

• \(2x - 6 = 24\) → 15
• \(2x + 6 = 24\) → 9
• \(2(x + 6) = 24\) → 6
• \(2(x - 6) = 24\) → 18

These are the solutions associated with the respective equations.

Answer 4

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Question
Match the correct mathematical expression with each phrase.

An answer choice may be used more than once or not at all.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
twice a number, increased by five
twice the difference of a number and five
twice the sum of a number and five
five decreased by twice a number
five less than twice a number
twice a number less five

2x - 5
2(x - 5)
5 - 2x
2x + 5
2 (x + 5)

Answer 5

Here are the matches between the phrases and the corresponding mathematical expressions:

1. Twice a number, increased by five
   Expression: \(2x + 5\)

2. Twice the difference of a number and five
   Expression: \(2(x - 5)\)

3. Twice the sum of a number and five
   Expression: \(2(x + 5)\)

4. Five decreased by twice a number
   Expression: \(5 - 2x\)

5. Five less than twice a number
   Expression: \(2x - 5\)

6. Twice a number less five
   Expression: \(2x - 5\)

So, summarizing the matches:

• Twice a number, increased by five → \(2x + 5\)
• Twice the difference of a number and five → \(2(x - 5)\)
• Twice the sum of a number and five → \(2(x + 5)\)
• Five decreased by twice a number → \(5 - 2x\)
• Five less than twice a number → \(2x - 5\)
• Twice a number less five → \(2x - 5\)

Feel free to adjust the organization according to your needs!

Answer 6

Solve the following equation for x.
4x - 6 = 8
x =

Answer 7

To solve the equation \(4x - 6 = 8\), follow these steps:

1. Add 6 to both sides: \[ 4x - 6 + 6 = 8 + 6 \] \[ 4x = 14 \]

2. Divide both sides by 4: \[ x = \frac{14}{4} \] \[ x = \frac{7}{2} \] \[ x = 3.5 \]

So, the solution is:

\[ x = 3.5 \]

Answer 8

Matthew and Anthony each have a video game collection.

• The number of video games in Matthew’s collection can be represented by x.
• The number of video games in Anthony’s collection is 5 times the number in Matthew’s collection.
• The total number of video games in both collections is 72.

What is x, the number of video games in Matthew’s collection?

Answer 9

To solve for \(x\), the number of video games in Matthew's collection, we can set up the equation based on the information given:

1. Let \(x\) be the number of video games in Matthew’s collection.
2. The number of video games in Anthony’s collection is \(5x\) (since it is 5 times the number in Matthew's collection).
3. The total number of video games in both collections is 72.

We can set up the equation as follows:

\[ x + 5x = 72 \]

Now, combine the terms on the left:

\[ 6x = 72 \]

Next, divide both sides by 6:

\[ x = \frac{72}{6} \]

\[ x = 12 \]

So, the number of video games in Matthew's collection is:

\[ \boxed{12} \]

Answer 10

Amari went to the mall and spent 47
. He bought one shirt for 26
and he bought 3 pairs of socks. Each pair of socks cost the same amount of money.

PART A

Write an equation that can be used to find the cost of each pair of socks. Use
x to represent the cost of each pair of socks.

Type your equation:

Answer 11

To find the cost of each pair of socks, we can set up the equation based on the information provided.

1. Amari spent a total of $47.
2. He bought one shirt for $26.
3. He bought 3 pairs of socks, each costing \(x\) dollars.

The total amount spent on the shirt and the socks can be expressed as:

\[ 26 + 3x = 47 \]

So, the equation that can be used to find the cost of each pair of socks is:

\[ 3x + 26 = 47 \]

You can type this equation:

3x + 26 = 47