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Solve the system of equations
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Arithmetic
Three companies can supply a university with some mathematical software. Each company has a different pricing structure: Company 1 provides a site licence which costs $130 000 and can be used by anyone at the university; Company 2 charges $1000 per user; Company 3 charges a fixed amount of $40 000 for the first 60 users and $500 for each additional user. (a) Draw a graph of each cost function on the same set of axes. (b) What advice can you give the university about which company to use?
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Arithmetic
Two new models of a smart phone are launched on 1 January 2018. Predictions of sales are given by: Model 1: S1 = 4 + 0.5n Model 2: S2 = 8 + 0.1n Where Si (in tens of thousands) denotes the monthly sales of model i after n months. State the values of the slope and intercept of each line and give an interpretation. Illustrate the sales of both models during the first year by drawing graphs on the same axes. Use the graph to find the month when sales of Model 1 overtake those of Model 2.
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Arithmetic
Find the point of intersection of the two lines 4x + 3y = 11 2x + y = 5
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Arithmetic
Sketch the line 2x + y = 5
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Arithmetic
Sketch the line 4x + 3y = 11
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Arithmetic
A firm’s Human Resources department has a budget of $25 000 to spend on training and laptops. Training courses cost $700 and new laptops are $1200. If the department trains E employees and buys L laptops, write down an inequality for E and L. If 12 employees attend courses, how many laptops could be bought?
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Arithmetic
Solve (a) 6x + 1 = 10x – 9 (b) 3(x − 1) + 2(2x + 1) = 4 (c) 20/(3x-1)=7 (d) 9/(x+2)=7/(2x+1) (e)√(2x/(x-6)=2)
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Arithmetic
