Mural Paint: Mixing, Coverage and Cost
A youth club is painting a rectangular mural on an outdoor wall. The mural is 8 m long and 3.5 m high. The club plans to apply two coats of paint. The paint label says one litre covers 10 m² per coat. The club will mix gloss paint with thinner in the ratio 4:1 by volume. To allow for spills and brush loss, they add 10% to the calculated paint volume before buying. Gloss paint is sold only in 5-litre tins at €38 each. Thinner is sold in 1-litre tins at €6.50 each. The club has no paint or thinner left over from previous projects. A parent has offered to buy any unused gloss at half price, but the club would rather avoid waste. The treasurer wants to know the total volume to mix, how much of each liquid is needed, and the cheapest way to buy the tins. All quantities must be bought in whole tins.
1. Calculate the area of the mural and the total paint volume needed for two coats, including the 10% allowance. Round your final volume sensibly.
Read the worked answer
Area of mural = length × height = 8 × 3.5 = 28 m².
Two coats means the paint must cover 2 × 28 = 56 m² in total.
Coverage is 10 m² per litre, so paint needed before wastage:
56 ÷ 10 = 5.6 litres.
Wastage allowance is 10%, so add 0.10 × 5.6 = 0.56 litres:
5.6 + 0.56 = 6.16 litres.
A sensible practical figure is about 6.2 litres, but the exact calculated volume is 6.16 litres. Use 6.16 litres in the ratio calculation so the parts add correctly.
2. Use the 4:1 ratio to find the litres of gloss and thinner required. Check that the parts add to the total.
Read the worked answer
The ratio gloss : thinner = 4 : 1, so there are 4 + 1 = 5 parts in total.
Total volume = 6.16 litres.
One part = 6.16 ÷ 5 = 1.232 litres.
Gloss = 4 parts = 4 × 1.232 = 4.928 litres.
Thinner = 1 part = 1.232 litres.
Check: 4.928 + 1.232 = 6.16 litres, which matches the total. The gloss is four times the thinner: 4.928 ÷ 1.232 = 4, so the ratio is correct.
3. Work out how many tins of each the club must buy, the total cost, and how much gloss is left. Is the parent's offer relevant?
Read the worked answer
Gloss: need 4.928 litres. Gloss is sold only in 5-litre tins, so buy 1 tin.
Cost = 1 × €38 = €38.00.
Gloss left = 5 − 4.928 = 0.072 litres (72 ml).
Thinner: need 1.232 litres. Thinner is sold in 1-litre tins, so buy 2 tins.
Cost = 2 × €6.50 = €13.00.
Thinner left = 2 − 1.232 = 0.768 litres (768 ml).
Total cost = 38.00 + 13.00 = €51.00.
The parent's offer is not really relevant. Only 0.072 litres of gloss is left, which is a negligible amount; selling it at half price would raise only about 5 cent and would not change the buying decision. The club cannot avoid buying the 5-litre gloss tin because a smaller tin is not sold.