Writing Equations with Variables on Both Sides

Flashcards for matching word problems to linear equations with variables on both sides.

What linear equation represents the following problem?

Jessica has $100 in her checking account and is depositing $5 per day. Dan has $200 in his checking account and is spending $4 per day. After how many days will they have the same amount of money?

$$100 + 5x = 200 - 4x$$

What linear equation represents the following problem?

Collin pays $9 for a movie ticket plus $3 per snack. Reese pays $12 for a movie ticket plus $2 per snack. After how many snacks will Collin and Reese have spent the same amount of money?

$$9 + 3x = 12 + 2x$$

What linear equation represents the following problem?

Waterpark A costs $60 for a season pass plus $15 per visit. Waterpark B costs $45 for a season pass plus $20 per visit. After how many visits will the waterparks cost the same amount of money?

$$60 + 15x = 45 + 20x$$

What linear equation represents the following problem?

Gage has 9 pieces of gum and gives away 2 pieces to each of his friends. Lily has 12 pieces of gum and gives away 3 pieces to each of her friends. How many friends will it take for Gage and Lily to have the same number of pieces of gum?

$$9 - 2x = 12 - 3x$$

What linear equation represents the following problem?

Carly's drone is 60 feet in the air and descending at a rate of 20 feet per minute. Reagan's drone is 45 feet in the air and is ascending at a rate of 15 feet per minute. After how many minutes will Carly and Reagan's drones be at the same height?

$$60 - 20x = 45 + 15x$$

What linear equation represents the following problem?

Ryan and David each buy an international phone plan. Ryan pays $5 per day plus a $100 fee. David pays $4 per day plus a $200 fee. After how many days will their plans cost the same amount of money?

$$100 + 5x = 200 + 4x$$

What linear equation represents the following problem?

In Alaska, the temperature is 9°F and is increasing at a rate of 3°F per hour. In Canada, the temperature is 12°F and is decreasing at a rate of 2°F per hour. After how many hours will the temperatures be the same?

$$9 + 3x = 12 - 2x$$

What linear equation represents the following problem?

Stephanie has $60 and is spending $15 per day. Felicia has $45 and is saving $20 per day. After how many days will Stephanie and Felicia have the same amount of money?

$$60 - 15x = 45 + 20x$$

What linear equation represents the following problem?

Alex has 200 tickets to an arcade that costs 5 tickets per game. Jeff has 100 tickets to an arcade that costs 4 tickets per game. After how many games will they have the same number of tickets?

$$100 - 4x = 200 - 5x$$

What linear equation represents the following problem?

Stella has $9 and earns $2 per day by doing the dishes for her mom. Lizzy has $12 and spends $3 each day on coffee. After how many days will Stella and Lizzy have the same amount of money?

$$9 + 2x = 12 - 3x$$

What linear equation represents the following problem?

Jensen has 60 pieces of candy and eats 20 pieces each day. Ben has 45 pieces of candy and eats 15 pieces each day. After how many days will Jensen and Ben have the same number of pieces of candy?

$$60 - 20x = 45 - 15x$$

What linear equation represents the following problem?

Noelle has 200 mL in her water bottle and is drinking 5 mL per second. Ashley has 100 mL in her water bottle and is filling it up at a rate of 4 mL per second. After how many seconds will they have the same amount of water in their bottles?

$$100 + 4x = 200 - 5x$$