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Q1 Question Points: 1

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Plan A charges $12\text{ dollars}$ plus $4\text{ dollars}$ per visit. Plan B charges $30\text{ dollars}$ plus $2\text{ dollars}$ per visit. If $v$ is the number of visits, which equation represents equal total costs, and how many visits make the costs equal?

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Q2 Question Points: 1

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Maya uses $\frac{1}{2}x+7$ metres of ribbon. Liam uses $\frac{3}{4}x-2$ metres. They use equal lengths. Which equation represents the situation, and what is $x$ ?

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Q3 Question Points: 1

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Five less than three times a number is equal to one more than twice the number. If the number is $n$ , which equation and solution represent this statement?

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Q4 Question Points: 1

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Two rectangles have equal perimeters. Rectangle A has length $(x+2)\text{ cm}$ and width $4\text{ cm}$ . Rectangle B has length $(2x-3)\text{ cm}$ and width $2\text{ cm}$ . Which equation represents the equal perimeters, and what is $x$ ?

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Q5 Question Points: 1

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Tank A contains $\left(\frac{3}{5}x+8\right)\text{ litres}$ of water. Tank B contains $\left(\frac{1}{4}x+22\right)\text{ litres}$ . The tanks contain equal amounts. Which equation represents this situation, and what is $x$ ?

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Q6 Question Points: 1

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Taxi P charges a starting fee of $6\text{ dollars}$ and $\frac{5}{2}\text{ dollars}$ per kilometre. Taxi Q charges a starting fee of $18\text{ dollars}$ and $\frac{3}{2}\text{ dollars}$ per kilometre. If $k$ is the distance travelled, which equation represents equal fares, and at what distance are they equal?

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Q7 Question Points: 1

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Subtracting $4$ from half a number gives the same result as adding $5$ to one third of the number. If the number is $y$ , which equation and solution represent the statement?

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Q8 Question Points: 1

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Zara starts with $4$ bags containing $c$ counters each and then gives away $7$ counters. Imran starts with $2$ identical bags and then receives $13$ counters. They finish with the same number of counters. Which equation represents the situation, and how many counters are in each bag?

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Q9 Question Points: 1

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The balance scale in the figure is level. Each bag has the same mass, represented by $m$ . Which equation represents the balance, and what is the mass of one bag?

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Q10 Question Points: 1

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The figure shows two bars with the same total length. Which equation represents their equal lengths, and what is $x$ ?

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