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Algebra for Preservation

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Algebra for Preservation

A fictional camping group is helping care for a patch of native bush beside its campsite. The group plans a small clean-up and seedling-care day. Use algebra to test the plan; all people, costs and quantities below are fictional. Show your working and include units in your answers.

Plan the preservation day

The group has a fixed budget and needs to estimate supplies before heading out.

1.Tane estimates that each volunteer will need 2 pairs of gloves. Write an expression for the number of individual gloves needed for v volunteers, and explain what v represents.

2.Mere packs 3 seedling trays, each holding (n + 4) seedlings. Which expression gives the total number of seedlings?

3n + 4
3n + 12
n + 12
7n

3.There are 9 volunteers. If each needs 2 pairs of gloves, evaluate your expression from Question 1. How many individual gloves is this, and how many pairs are needed?

4.A bundle of rubbish bags costs $6, and each pair of gloves costs $4. The group spends $42 on these items. If g is the number of glove pairs, write and solve an equation to find g.

Model the growing work

The group records how many seedlings it can water as it adds volunteers. Assume every volunteer waters the same number of seedlings.

Volunteers

Seedlings watered

5.Let v be the number of volunteers and s the number of seedlings watered. Use the table to write a rule connecting s and v.

6.Using your rule from Question 5, how many seedlings can 7 volunteers water? Show the calculation and include the unit.

7.Plan A waters 8 seedlings per volunteer. Plan B waters 6 seedlings per volunteer, plus 10 seedlings prepared before the trip. Write an expression for each plan when there are v volunteers. At how many volunteers do the plans water the same number?

Check feasibility and explain

A model helps with planning, but its assumptions need to be checked against real conditions on the day.

8.The group has $50 for gloves. Gloves cost $4 per pair. Write an inequality for the greatest number g of pairs it can buy, then find the greatest whole-number value of g.

9.The group assumes every volunteer waters the same number of seedlings. Give one realistic reason that this prediction might not match the actual number watered on a camping trip.