When are two plans equal? Equations from real comparisons

Question 1

Candle A is 20 cm tall and burns 3 cm per hour. Candle B is 4 cm tall and burns 1 cm per hour. After how many hours are they the same height?

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Question 2

Kofi has $8 and saves $6 a week. Felix has nothing yet and saves $8 a week. After how many weeks will they have the same amount?

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Question 3

Gym A charges $55 to join plus $4 per visit. Gym B charges $10 to join plus $7 per visit. For how many visits do they cost the same?

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Question 4

Candle A is 24 cm tall and burns 4 cm per hour. Candle B is 3 cm tall and burns 1 cm per hour. After how many hours are they the same height?

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Question 5

Nia has $10 and saves $3 a week. Kwame has nothing yet and saves $4 a week. After how many weeks will they have the same amount?

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Question 6

Gym A charges $40 to join plus $6 per visit. Gym B charges $7 to join plus $9 per visit. For how many visits do they cost the same?

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Question 7

Candle A is 26 cm tall and burns 5 cm per hour. Candle B is 16 cm tall and burns 3 cm per hour. After how many hours are they the same height?

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Question 8

Omar has $48 and saves $3 a week. Fatima has nothing yet and saves $7 a week. After how many weeks will they have the same amount?

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Question 9

Streaming plan A costs $37 up front plus $2 per film. Plan B costs $11 up front plus $4 per film. For how many films do they cost the same?

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Question 10

Candle A is 36 cm tall and burns 5 cm per hour. Candle B is 28 cm tall and burns 3 cm per hour. After how many hours are they the same height?

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Question 11

Zara has $48 and saves $5 a week. Mateo has nothing yet and saves $9 a week. After how many weeks will they have the same amount?

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Question 12

Gym A charges $54 to join plus $4 per visit. Gym B charges $2 to join plus $8 per visit. For how many visits do they cost the same?

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Question 13

Candle A is 37 cm tall and burns 5 cm per hour. Candle B is 21 cm tall and burns 3 cm per hour. After how many hours are they the same height?

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Question 14

Leo has $16 and saves $4 a week. Zara has nothing yet and saves $8 a week. After how many weeks will they have the same amount?

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Question 15

Gym A charges $17 to join plus $5 per visit. Gym B charges $11 to join plus $7 per visit. For how many visits do they cost the same?

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Question 16

Candle A is 30 cm tall and burns 3 cm per hour. Candle B is 14 cm tall and burns 1 cm per hour. After how many hours are they the same height?

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