A building firm splits the cost of hiring a cement mixer between two site teams for a foundation job. Team A pays \(\frac{x}{3}\) of the total cost, and Tea...
Question 1 Report
A building firm splits the cost of hiring a cement mixer between two site teams for a foundation job. Team A pays \(\frac{x}{3}\) of the total cost, and Team B pays \(\frac{x}{3} + 40\) pounds, where \(x\) is the total cost in pounds. Together the teams cover the full amount, so \(\frac{x}{3} + \frac{x}{3} + 40 = x\). Solve this equation to find \(x\). (5)
Answer Details
An equation containing fractions is solved most efficiently by first multiplying every term by the common denominator, which clears every fraction from the equation in one step.
Multiplying every term of \(\frac{x}{3} + \frac{x}{3} + 40 = x\) by 3 clears both fractions: \[x + x + 120 = 3x\] [2 marks]
Collecting the two terms in \(x\) on the left gives \[2x + 120 = 3x\] [1 mark]
Subtracting \(2x\) from both sides isolates the constant: \[120 = x\] [1 mark]
So the total cost is \[x = \pounds120\] [1 mark]
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