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pick which equation matches the most

1. Darius is 38 years old. in 4 years he will be 3 times as old as Gia. how old is Gia?:
2. i think of a number, multiply it by 3 and then add four to get 42. what number am i thinking of :
3. 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:
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?:
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?:
a. 3x+4=42
b. 3x+20=38
c. 4x+2=38
d. 3(x+4) =42
e. 4(x+3)-=42

5 answers

Let's analyze each problem to determine which equation matches best.

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

    • In 4 years, Darius will be \(38 + 4 = 42\). Let Gia's age be \(g\). According to the problem, \(42 = 3g\). Thus, Gia's age is \(g = 14\). The equation can be written as \(3g = 42\), which simplifies to \(g = 14\).

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

    • Let the number be \(x\). The equation is \(3x + 4 = 42\) which simplifies to \(3x = 38\).

  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?

    • Let the number of paints be \(p\). The equation is \(20 + 3p = 38\), which simplifies to \(3p = 18\) or \(p = 6\).

  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?

    • Let the number of weeks be \(w\). Chelsea's debt decreases as \(4w\). The equation can be set up as \(38 - 4w = 2\), which simplifies to \(4w = 36\).

  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 \(x\)?

    • The area of a rectangle is given by the product of length and width: \(4(x + 3) = 42\).

Now, let's match the equations:

  • For problem 1: \(3g = 42\) (not listed).
  • For problem 2: \(3x + 4 = 42\) (matches option b: \(3x + 20 = 38\) does not match).
  • For problem 3: \(20 + 3p = 38\) (not listed).
  • For problem 4: \(38 - 4w = 2\) (not listed).
  • For problem 5: \(4(x + 3) = 42\) (matches option e: \(4(x + 3) = 42\) but using '–=' seems to be an error).

The choices of equations presented:

  • a. 3x + 4 = 42 (correct for problem 2)
  • b. 3x + 20 = 38 (not applicable)
  • c. 4x + 2 = 38 (not applicable)
  • d. 3(x + 4) = 42 (not applicable)
  • e. 4(x + 3) = 42 (correct for problem 5, but seems to have a typo).

Based on the analysis, the correct matches are: 2 (3x + 4 = 42) from problem 2 and 5 (4(x + 3) = 42) from problem 5.

If we had to choose the best overall match, I would pick option a for problem 2 as most directly related.

can u pick for all of them?

Sure! Let's match each of the original problems with the provided equations:

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

    • Equation: This can be expressed as \( 38 + 4 = 3g \) or \( 42 = 3g \). None of the provided options match this directly.
    • Best Match: None of the provided options.

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

    • Equation: \( 3x + 4 = 42 \).
    • Best Match: a. \( 3x + 4 = 42 \).

  3. Problem: 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: The equation can be set up as \( 20 + 3p = 38 \), which simplifies to \( 3p = 18 \).
    • Best Match: None of the provided options.

  4. Problem: 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: This can be expressed as \( 38 - 4w = 2 \) or \( 4w = 36 \).
    • Best Match: None of the provided options.

  5. Problem: 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: The area is given by \( 4(x + 3) = 42 \).
    • Best Match: e. \( 4(x + 3) = 42 \).

Summary of Matches:

  1. Darius & Gia: None
  2. Number problem: a. \( 3x + 4 = 42 \)
  3. Lucia's paints: None
  4. Chelsea's repayment: None
  5. Rectangle area: e. \( 4(x + 3) = 42 \)

Let me know if you need any further clarification!

just pick for all of them pleasee

Sure! Here’s the direct matching for all the problems with the provided options:

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

    • Best Match: None

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

    • Best Match: a. \( 3x + 4 = 42 \)

  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?

    • Best Match: None

  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?

    • Best Match: None

  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 \(x\)?

    • Best Match: e. \( 4(x + 3) = 42 \)

Final Matches:

  1. None
  2. a. \(3x + 4 = 42\)
  3. None
  4. None
  5. e. \(4(x + 3) = 42\)

Thank you for your patience! If you have further questions or need any additional assistance, feel free to ask!