Algebra: Take The Linear Equation Test Quiz!

1. Willie rented a bike from Beach Bikes. It costs $18 plus $5 for each hour. If Willie paid $48 when he returned his bike, how many hours did he rent the bike?Let x = the hours he rented the bike.

18x + 5 = 48

48 - 5 = 18x

18 + 5x = 48

None of these

The correct answer is 18 + 5x = 48. This equation represents the cost of renting the bike, where x is the number of hours. The equation states that the cost of renting the bike for x hours, which is 18x, plus the initial cost of $18, should equal $48, the amount Willie paid when he returned the bike.

Explanation

The correct answer is 18 + 5x = 48. This equation represents the cost of renting the bike, where x is the number of hours. The equation states that the cost of renting the bike for x hours, which is 18x, plus the initial cost of $18, should equal $48, the amount Willie paid when he returned the bike.

2. There were seven roses in the vase. Sara cut some more roses from her flower garden. There are now 16 roses in the vase. How many roses did she cut? Let r = # of roses she cut.

R + 7 = 16

R - 7 = 16

7r = 16

None of these

The equation r + 7 = 16 represents the number of roses Sara cut. By subtracting 7 from both sides of the equation, we can find the value of r. Therefore, the answer is r + 7 = 16.

Explanation

The equation r + 7 = 16 represents the number of roses Sara cut. By subtracting 7 from both sides of the equation, we can find the value of r. Therefore, the answer is r + 7 = 16.

3. The local dog groomer charges $18 for a dog bath and $3 for each special service. If Jonah's total bill was $27, how many special services were included? Let x = # of special services

18 - 27 = 3x

27 = 18 + 3x

27 + 3x = 18

None of these

The given equation is incorrect. The correct equation should be 27 = 18 + 3x. This equation represents the total bill of $27 being equal to the base charge of $18 plus the additional charge for each special service, which is $3 multiplied by the number of special services (x).

Explanation

The given equation is incorrect. The correct equation should be 27 = 18 + 3x. This equation represents the total bill of $27 being equal to the base charge of $18 plus the additional charge for each special service, which is $3 multiplied by the number of special services (x).

4. How many ink cartridges can you buy for 105 dollars if one cartridge costs 15 dollars? Let c= the number of ink cartridges you can buy.

15 - 105 = c

105 = c - 15

15 = 105 + c

None of these

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Explanation

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5. Solve: 5(y - 1) = 3(2y - 5) - (1 - 3y)

1/2

8/12

23/11

11/4

The correct answer is 11/4. To solve the equation, we first distribute the terms on the right side of the equation: 5(y - 1) = 3(2y - 5) - (1 - 3y). This simplifies to 5y - 5 = 6y - 15 - 1 + 3y. Combining like terms, we have 5y - 5 = 9y - 16. Next, we isolate the variable by subtracting 9y from both sides and adding 5 to both sides: -4y = -11. Finally, we solve for y by dividing both sides by -4, resulting in y = 11/4.

Explanation

The correct answer is 11/4. To solve the equation, we first distribute the terms on the right side of the equation: 5(y - 1) = 3(2y - 5) - (1 - 3y). This simplifies to 5y - 5 = 6y - 15 - 1 + 3y. Combining like terms, we have 5y - 5 = 9y - 16. Next, we isolate the variable by subtracting 9y from both sides and adding 5 to both sides: -4y = -11. Finally, we solve for y by dividing both sides by -4, resulting in y = 11/4.

6. Solve: (0.5y - 9)/0.25 = 4y - 3

-5.4

-7.8

-16.5

-18.2

To solve the given equation, we can start by multiplying both sides of the equation by the denominator, which is 0.25. This eliminates the fraction on the left side of the equation. Simplifying the equation, we get 2y - 36 = 4y - 3. Next, we can move all the terms with y to one side of the equation and the constant terms to the other side. This gives us 2y - 4y = -3 + 36. Simplifying further, we have -2y = 33. Finally, dividing both sides of the equation by -2, we get y = -16.5. Therefore, the correct answer is -16.5.

Explanation

To solve the given equation, we can start by multiplying both sides of the equation by the denominator, which is 0.25. This eliminates the fraction on the left side of the equation. Simplifying the equation, we get 2y - 36 = 4y - 3. Next, we can move all the terms with y to one side of the equation and the constant terms to the other side. This gives us 2y - 4y = -3 + 36. Simplifying further, we have -2y = 33. Finally, dividing both sides of the equation by -2, we get y = -16.5. Therefore, the correct answer is -16.5.

7. Solve: (3y - 2)/3 + (2y + 3)/3 = (y + 7)/6

4/7

5/9

2/3

6/25

To solve the given equation, we need to combine like terms on both sides of the equation. The left side of the equation can be simplified by adding the fractions with a common denominator of 3. This gives us (5y + 1)/3 = (y + 7)/6. To eliminate the fractions, we can cross-multiply to get 6(5y + 1) = 3(y + 7). Simplifying this further, we have 30y + 6 = 3y + 21. By subtracting 3y from both sides and subtracting 6 from both sides, we get 27y = 15. Dividing both sides by 27, we find that y = 15/27, which simplifies to 5/9. Therefore, the correct answer is 5/9.

Explanation

To solve the given equation, we need to combine like terms on both sides of the equation. The left side of the equation can be simplified by adding the fractions with a common denominator of 3. This gives us (5y + 1)/3 = (y + 7)/6. To eliminate the fractions, we can cross-multiply to get 6(5y + 1) = 3(y + 7). Simplifying this further, we have 30y + 6 = 3y + 21. By subtracting 3y from both sides and subtracting 6 from both sides, we get 27y = 15. Dividing both sides by 27, we find that y = 15/27, which simplifies to 5/9. Therefore, the correct answer is 5/9.

8. Solve: (2x - 5)/(3x - 1) = (2x - 1)/(3x + 2)

-11/6

6/11

9/7

16/5

To solve the given equation, we can start by cross-multiplying. This gives us (2x - 5)(3x + 2) = (2x - 1)(3x - 1). Expanding both sides of the equation, we get 6x^2 - 11x - 10 = 6x^2 - 5x - 2. Simplifying the equation, we have -11x - 10 = -5x - 2. By isolating the variable, we get -11x + 5x = -2 + 10. Combining like terms, we have -6x = 8. Dividing both sides by -6, we get x = -8/6 or x = -4/3. Therefore, the correct answer is -11/6.

Explanation

To solve the given equation, we can start by cross-multiplying. This gives us (2x - 5)(3x + 2) = (2x - 1)(3x - 1). Expanding both sides of the equation, we get 6x^2 - 11x - 10 = 6x^2 - 5x - 2. Simplifying the equation, we have -11x - 10 = -5x - 2. By isolating the variable, we get -11x + 5x = -2 + 10. Combining like terms, we have -6x = 8. Dividing both sides by -6, we get x = -8/6 or x = -4/3. Therefore, the correct answer is -11/6.

9. Jason received 66 dollars for his birthday. He went to a sporting goods store and bought a baseball glove, baseball, and bat. He had 20 dollars left over. How much did he spend on the baseball gear? Let g = the amount he spent on the gear.

66 + 20 = g

G + 66 = 20

G + 20 = 66

None of these

The given equation g + 20 = 66 represents the amount Jason spent on the baseball gear. By subtracting 20 from both sides of the equation, we get g = 66 - 20, which simplifies to g = 46. Therefore, Jason spent 46 dollars on the baseball gear.

Explanation

The given equation g + 20 = 66 represents the amount Jason spent on the baseball gear. By subtracting 20 from both sides of the equation, we get g = 66 - 20, which simplifies to g = 46. Therefore, Jason spent 46 dollars on the baseball gear.

10. Write in slope intercept form: 5x - 3y = -9.

Y = (5/3)x + 3

Y = (5/3)x + 9

Y = (5/3)x - 3

Y = (3/5)x + 3

The given equation, 5x - 3y = -9, can be rewritten in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. By isolating the y term, we can rearrange the equation to y = (5/3)x + 3. This means that the slope of the line is 5/3 and the y-intercept is 3.

Explanation

The given equation, 5x - 3y = -9, can be rewritten in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. By isolating the y term, we can rearrange the equation to y = (5/3)x + 3. This means that the slope of the line is 5/3 and the y-intercept is 3.