SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES Flashcard

Front

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?

Back

5 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.

Front

Emily is at 2,700 feet, descending at 85 feet/min. Mark is at 1,500 feet, ascending at 35 feet/min. How many minutes until they are at the same height?

Back

20 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.

Front

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

Back

10 weeks

Answer explanation

This is an example explanation.

Front

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?

Back

6 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.

Front

Sierra's bucket: 340 fl oz + 5 fl oz/min. Brian's bucket: 650 fl oz - 8 fl oz/min. When will they have the same amount of water?

Back

60 minutes

Answer explanation

Insert your answer explanation here.

Front

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

Back

x = 4

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.

Front

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

Back

True

Answer explanation

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

Front

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. Write an equation to find how many pieces she started with.

Back

(x-10)/4=2

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.

Front

First step to solve the equation: -11 - 3x = 44 - 2x

Back

Get the variables on one side

Answer explanation

Get the variables on one side

Front

7x = 4x + 33

Back

x = 11

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.