A library is buying new shelving. A tall unit holds \(2(r + 3)\) books and a short unit holds \((r + 9)\) books, where \(r\) is a whole number. One tall uni...
Question 1 Report
A library is buying new shelving. A tall unit holds \(2(r + 3)\) books and a short unit holds \((r + 9)\) books, where \(r\) is a whole number. One tall unit and one short unit together hold 33 books. Form and solve an equation to find \(r\). (4)
Answer Details
This question expands an algebraic expression for one shelving unit, combines it with another expression, and solves the resulting linear equation.
Expanding the tall unit's capacity:
\[2(r+3) = 2r+6\][1 mark]
Adding the short unit's capacity, \((r+9)\), and setting the total equal to \(33\):
\[2r+6+r+9 = 33\] \[3r + 15 = 33\][1 mark]
Subtracting \(15\) from both sides:
\[3r = 18\][1 mark]
Dividing by \(3\):
\[r = 6\][1 mark]
Checking: the tall unit holds \(2(6+3)=18\) books and the short unit holds \(6+9=15\) books, giving \(18+15=33\) books in total, which matches.
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