SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES Quiz

A minor league baseball team has a member’s club. It costs $25 to join and $5 per ticket. Non-members pay $10 per ticket. How many tickets will it take for the cost to be the same?

• A) 3 tickets

• B) 5 tickets

• C) 7 tickets

• D) 10 tickets

Answer explanation

To find the number of tickets needed for the cost to be the same, set the equations 25 + 5x = 10x. Solving for x gives x = 5, so it will take 5 tickets for the cost to be the same.

Emily and Mark are both on a mountain hike. Emily is currently at 2,700 feet and descending at a rate of 85 feet per minute. Mark is currently at 1,500 feet and ascending at a rate of 35 feet per minute. How many minutes will it take for Emily and Mark to be at the same height?

• A) 10 minutes

• B) 15 minutes

• C) 20 minutes

• D) 30 minutes

Answer explanation

To find the time it takes for Emily and Mark to be at the same height, we need to determine when their altitudes will be equal. The time can be calculated by setting their altitudes equal to each other and solving for time. This gives us 2700 - 85t = 1500 + 35t. Solving for t, we get t = 20 minutes. Therefore, it will take 20 minutes for Emily and Mark to be at the same height. Hence, the correct answer is C) 20 minutes.

Chris has $250 in his savings account and is saving $30 each week. Robert has $475 in his savings account and is saving $15 per week. How many weeks will it take Chris and Robert to have the same amount of money in their savings accounts?

• A) 5 weeks

• B) 10 weeks

• C) 15 weeks

• D) 20 weeks

Answer explanation

This is an example explanation.

The Seattle Express train costs $3 per ride. They also have a train pass that is $10 plus $0.50 per ride. How many rides would it take for the cost to be the same?

• A) 2 rides

• B) 4 rides

• C) 6 rides

• D) 8 rides

Answer explanation

To find the number of rides where the cost is the same, set the equations 3x = 10 + 0.5x. Solving for x gives x = 6 rides. Therefore, it would take 6 rides for the cost to be the same.

Sierra has a bucket that originally contained 340 fl oz of water and is being filled at a rate of 5 fl oz per minute. Brian has a bucket that originally contained 650 fl oz of water and is being drained at a rate of 8 fl oz per minute. What is x, the number of minutes that need to pass in order for the two buckets to contain the same amount of water?

• A) 30 minutes

• B) 40 minutes

• C) 50 minutes

• D) 60 minutes

Answer explanation

Insert your answer explanation here.

Solve the equation
12x - 15 = 3(2x+3)

• x = 4

• x = -4

• x = 2

• x = -2

Answer explanation

To solve the equation, first distribute the 3 on the right side: 12x - 15 = 6x + 9. Then, isolate x by moving 6x to the left side: 12x - 6x = 9 + 15. Simplify to get 6x = 24, and divide by 6 to find x = 4.

In order to solve an equation, we must get variables on side of an equation, and constants on the opposite side.

• True

• False

Answer explanation

True because to solve an equation, variables must be isolated on one side and constants on the other side.

WRITE AN EQUATION
Aliyah had some candy to give to her four children. She first took ten pieces for herself and then evenly divided the rest among her children. Each child received two pieces. With how many pieces did she start?

• (x-10)/4=2

• x-10/4=2

• x-10=2(4)

• 2(x-10)=4

Answer explanation

The correct equation is (x-10)/4=2 because Aliyah took 10 pieces for herself and divided the rest equally among her 4 children, each receiving 2 pieces.

Which statement best describes the first step to the equation?

-11- 3x = 44 - 2x

• Add 3 to both sides

• Add 11 to both sides

• Get the variables on one side

• Add 2 to both sides

Answer explanation

Get the variables on one side

7x = 4x + 33

• x = 3

• x = 11

• x = 21

• x = 88

Answer explanation

To solve the equation, subtract 4x from both sides to get 3x = 33. Then divide by 3 to find x = 11, which is the correct answer.