Answers should be given as integers or simplified fractions (do NOT use decimals).
2(2???? + 4) = −
(3???? + 6)
???? = 24????????(???? − ????)
Where ???? is the mass of the pipe in tonnes (t), ???? is the length, ???? is the outside diameter, and ???? is the wall thickness of the pipe, all measured in metres (m).
Use mathematics to explain how you determined your answer.
(i) Complete the equation below to represent the total monthly cost, C, of this mobile plan. Define any other variables that you use.
(ii) Use your equation to find how many text messages were sent in the last month if the bill came to $67.50.
Write an equation to show the length of L in terms of T (e.g. L=…)
(ii) The River Derwent is 249 km long, and if you double this length you
have triple the length of the River Tamar and River Leven combined.
Convert this sentence into an algebraic equation using the same
variables as above.
(iii) Combine your equations and solve to find the length of the River Tamar.
To stimulate his daughter in the pursuit of problem solving, a maths teacher offered to pay her $10 for every question she solved correctly, and to fine her $7 for every incorrect solution. After she had completed 32 problems the maths teacher was starting to regret his decision, he now owed his daughter $133! Use algebraic techniques to find out how many problems the daughter solved correctly.
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