When are two plans equal? Equations from real comparisons

Question 1

Gym A charges $46 to join plus $4 per visit. Gym B charges $10 to join plus $8 per visit. For how many visits do they cost the same?

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Question 2

Candle A is 35 cm tall and burns 6 cm per hour. Candle B is 11 cm tall and burns 3 cm per hour. After how many hours are they the same height?

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Question 3

Sofia has $36 and saves $6 a week. Amara has nothing yet and saves $10 a week. After how many weeks will they have the same amount?

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Question 4

Streaming plan A costs $32 up front plus $2 per film. Plan B costs $10 up front plus $4 per film. For how many films do they cost the same?

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Question 5

Candle A is 30 cm tall and burns 4 cm per hour. Candle B is 16 cm tall and burns 2 cm per hour. After how many hours are they the same height?

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Question 6

Kai has $4 and saves $2 a week. Nia has nothing yet and saves $4 a week. After how many weeks will they have the same amount?

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Question 7

Streaming plan A costs $24 up front plus $3 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 8

Candle A is 33 cm tall and burns 4 cm per hour. Candle B is 25 cm tall and burns 2 cm per hour. After how many hours are they the same height?

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Question 9

Luis has $12 and saves $6 a week. Ava has nothing yet and saves $7 a week. After how many weeks will they have the same amount?

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Question 10

Gym A charges $69 to join plus $2 per visit. Gym B charges $13 to join plus $6 per visit. For how many visits do they cost the same?

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Question 11

Candle A is 28 cm tall and burns 6 cm per hour. Candle B is 22 cm tall and burns 3 cm per hour. After how many hours are they the same height?

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Question 12

Hiro has $6 and saves $4 a week. Priya has nothing yet and saves $6 a week. After how many weeks will they have the same amount?

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Question 13

Streaming plan A costs $21 up front plus $3 per film. Plan B costs $6 up front plus $4 per film. For how many films do they cost the same?

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Question 14

Candle A is 33 cm tall and burns 2 cm per hour. Candle B is 28 cm tall and burns 1 cm per hour. After how many hours are they the same height?

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Question 15

Noah has $28 and saves $3 a week. Felix has nothing yet and saves $7 a week. After how many weeks will they have the same amount?

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Question 16

Streaming plan A costs $45 up front plus $5 per film. Plan B costs $0 up front plus $10 per film. For how many films do they cost the same?

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