A farmer plants maize and beans across two fields, North Field and South Field, using 75 hectares in total. The two-way table shows some of the areas plante...
Question 1 Report
A farmer plants maize and beans across two fields, North Field and South Field, using 75 hectares in total. The two-way table shows some of the areas planted, in hectares. Maize in South Field covers \(m\) hectares.
| North Field | South Field | Total | |
|---|---|---|---|
| Maize | 22 | \(m\) | 40 |
| Beans | 19 | 35 | |
| Total | 75 |
- Form an equation in \(m\) and solve it. (2)
- Work out the total area planted in North Field. (3)
Answer Details
This question tests forming a simple equation from a column total in a two-way table, then filling in a further missing cell to find a row total.
Part (a) [2] Maize's column total is \(40\), made up of \(22\) hectares in North Field and \(m\) hectares in South Field, so \(m+22=40\). Solving gives \(m=40-22=18\) hectares.
Part (b) [3] Beans in North Field are the Beans total minus Beans in South Field: \(35-19=16\) hectares. North Field's total area is Maize in North Field plus Beans in North Field: \(22+16=38\) hectares.
As a check, South Field's total is \(18+19=37\) hectares, and \(38+37=75\) hectares, matching the farm's overall total; this kind of cross-check confirms a two-way table has been completed correctly.
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