Section 4.4 - Solving For A Variable In A Linear Relation

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  • 1/10 Questions

    Farmer Bill has chickens and horses.  He has a total of 30 animals.  There are a total of 80 legs.  Each chicken has 2 legs and each horse has 4 legs.  How many of each type of animal does he have?

    • 20 chickens and 10 horses
    • 15 chickens and 15 horses
    • 10 chickens and 20 horses
    • 30 chickens
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About This Quiz

This quiz focuses on solving linear equations for a specific variable, covering basic to complex rearrangements and understanding inverse operations.

Linear Equations Quizzes & Trivia

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  • 2. 

    Consider the equation V = LWH.  What inverse operation would you use to solve for W?

    • Addition

    • Subtraction

    • Multiplication

    • Division

    Correct Answer
    A. Division
    Explanation
    To solve for W in the equation V = LWH, we need to isolate W on one side of the equation. Since W is being multiplied by L and H, the inverse operation to undo this multiplication is division. By dividing both sides of the equation by LH, we can cancel out the LH on the right side and be left with W on its own, solving for W. Therefore, the correct inverse operation to solve for W is division.

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  • 3. 

    Libby has $1.85 in quarters and dimes.  She has 11 coins in all.  How many of each does she have?

    • 5 dimes, 6 quarters

    • 6 dimes, 5 quarters

    • 2 dimes, 9 quarters

    • 4 dimes, 7 quarters

    Correct Answer
    A. 6 dimes, 5 quarters
    Explanation
    Libby has a total of 11 coins, and the total value of these coins is $1.85. Let's assume she has x dimes and y quarters. The value of x dimes is 0.10x, and the value of y quarters is 0.25y. Since Libby has a total of 11 coins, we can write the equation x + y = 11. Similarly, the total value of the coins is $1.85, so we can write the equation 0.10x + 0.25y = 1.85. By solving these two equations simultaneously, we find that x = 6 and y = 5, which means Libby has 6 dimes and 5 quarters.

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  • 4. 

    Solve A = (L)(W) for L

    • W = A/L

    • A = (L)(W)

    • L = (A)(W)

    • L = A/W

    Correct Answer
    A. L = A/W
    Explanation
    The given equation A = (L)(W) can be rearranged to solve for L. By dividing both sides of the equation by W, we get L = A/W. This means that in order to find the value of L, we need to divide the value of A by the value of W.

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  • 5. 

    Consider the equation C = 75 + 50t where C represents the cost for a plumer to do a job that takes t hours.  Why might someone want to rearrange the equation so that it is solved for t?

    • They want to hire a plumber for 10h

    • They want to know how many hours the plumber could work for a certain cost

    • They want to know the cost of a job

    • They want to hire an electrician for t hours

    Correct Answer
    A. They want to know how many hours the plumber could work for a certain cost
    Explanation
    Rearranging the equation to solve for t would allow someone to determine how many hours the plumber could work for a certain cost. By isolating the variable t, they can input a specific cost value into the equation and solve for t, giving them the number of hours the plumber could work for that cost. This would provide them with information on the amount of work they can expect from the plumber within their budget.

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  • 6. 

    Solve P = 2L + 2W for W

    • W = P - 2L

    • W = (P - 2L) / 2

    • W = P - L

    • W = L

    Correct Answer
    A. W = (P - 2L) / 2
    Explanation
    The correct answer is W = (P - 2L) / 2 because in the given equation P = 2L + 2W, we need to solve for W. To isolate W, we can start by subtracting 2L from both sides of the equation, which gives us P - 2L = 2W. Then, we divide both sides of the equation by 2 to solve for W, resulting in (P - 2L) / 2 = W.

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  • 7. 

    Solve 3x + 2y = 6 for y in terms of x

    • Y = -3/2x + 6

    • Y = x + 3

    • Y = -3/2x + 3

    • Y = -3x + 6

    Correct Answer
    A. Y = -3/2x + 3
    Explanation
    The correct answer is y = -3/2x + 3. This is the correct answer because it is obtained by rearranging the given equation 3x + 2y = 6 to solve for y. By subtracting 3x from both sides of the equation and then dividing by 2, we isolate y and obtain y = -3/2x + 3.

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  • 8. 

    If you multiply a number x by n and then add m the result is p.  What is the first inverse operation you should perform to solve this equation for x?

    • Multiply by m

    • Divide by m

    • Add m

    • Subtract m

    Correct Answer
    A. Subtract m
    Explanation
    To solve the equation for x, we need to undo the operations that were performed on x. The first inverse operation we should perform is to subtract m. By subtracting m, we can isolate the term that was added to x and undo its effect. This will help us find the original value of x before the multiplication and addition were performed.

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  • 9. 

    Solve 3/4x + 1/2y = 3 for y in terms of x

    • Y = -3/2x + 6

    • Y = -3x + 3

    • Y = -3/2x + 12

    • Y = 3x + 3

    Correct Answer
    A. Y = -3/2x + 6
    Explanation
    The given equation is 3/4x + 1/2y = 3. To solve for y in terms of x, we need to isolate y on one side of the equation. By subtracting 3/4x from both sides, we get 1/2y = -3/4x + 3. To get rid of the fraction, we can multiply both sides by 2, which gives us y = -3/2x + 6. Therefore, the correct answer is y = -3/2x + 6.

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  • 10. 

    If the area of a traingle is 15cm^2, and the height is 6cm, what is the base?

    • 5 cm

    • 6 cm

    • 5/2 cm

    • 30 cm

    Correct Answer
    A. 5 cm
    Explanation
    The area of a triangle is calculated by multiplying the base by the height and dividing by 2. In this case, the area is given as 15cm^2 and the height is given as 6cm. To find the base, we can rearrange the formula and solve for it. Base = (2 * Area) / height = (2 * 15cm^2) / 6cm = 30cm / 6cm = 5cm. Therefore, the base of the triangle is 5cm.

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  • Current Version
  • Mar 15, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Oct 15, 2008
    Quiz Created by
    Seixeiroda
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