All 303 families

CH-01-001 · Ratio, percentages and whole-pack purchasing

A club orders 2300 badges. The ratio of blue badges to green badges is 7:3. It already has 20% of the blue badges it needs. Extra blue badges are sold only in packs of 9, costing £6 per pack. Work out the least amount the club must spend on extra blue badges. Show all your working.

Ratio Table & Percentage Purchasing Application of booklet p. 18 & p. 51
Method
1) Use a ratio table
2) Find the remaining percentage
3) Divide by pack size and round up
4) Find the cost
Worked Example (CH-01-001)
1)
Use a ratio table. One part represents 2300÷(7+3)=2302300\div(7+3)=230 badges.
2)
Ratio partsActual badges (× 230)
Blue71610
Green3690
Total102300
3)
Find the percentage still needed: 80% of 1610=1610×80100=128880\%\text{ of }1610=1610\times\frac{80}{100}=1288 blue badges.
4)
Only whole packs can be bought. Round up: ⌈1288÷9⌉=144\left\lceil1288\div9\right\rceil=144 packs.
5)
Cost: 144×6=864.00144\times6=864.00 pounds.
Ans = £864.00