form 3 maths
2007-10-11 2:58 am
23.In the cost of cigarettes,12.5% is on raw materials,37.5% on labour and 50% on advertisement.If both the material cost and labour cost are increased by 10% while advertisement cost is decreased by5%,find the percentage change in the cost of cigarettes.
回答 (2)
2007-10-11 3:02 am
✔ 最佳答案
cost of cigarette = xcost of raw materials = 12.5% x = 0.125x
cost of labour = 37.5% x = 0.375x
cost of advertisement = 50% x = 0.5x
new cost of raw materials = 0.125x (1+10%) =0.1375x
new cost of labour = 0.375x (1+10%) = 0.4125x
new cost of advertisement = 0.5x (1-5%) = 0.475x
new cost of cigarette = 0.1375x + 0.4125x + 0.475x = 1.025x
percentage change
= (1.025x - x)/x * 100%
= 2.5%
2007-10-11 3:08 am
Let z be the cost:
therefore:
cost on raw materials = 0.125z
cost on labour = 0.375z
cost on advertisement = 0.5z
New cost:
on raw materials = 0.125z * 1.1 = 0.1375z
on labour = 0.375z * 1.1 = 0.4125z
on advertisement = 0.5z * 0.95 = 0.475z
Overall cost:
= (0.1375 + 0.4125 + 0.475 ) z
= 1.025z
Percentage Change:
= (New cost - Old cost) / (Old cost) * 100%
= ( 1.025z - z) / ( z ) * 100%
= 0.025 * 100%
= 2.5%
Therefore, the percentage change is 2.5%.
therefore:
cost on raw materials = 0.125z
cost on labour = 0.375z
cost on advertisement = 0.5z
New cost:
on raw materials = 0.125z * 1.1 = 0.1375z
on labour = 0.375z * 1.1 = 0.4125z
on advertisement = 0.5z * 0.95 = 0.475z
Overall cost:
= (0.1375 + 0.4125 + 0.475 ) z
= 1.025z
Percentage Change:
= (New cost - Old cost) / (Old cost) * 100%
= ( 1.025z - z) / ( z ) * 100%
= 0.025 * 100%
= 2.5%
Therefore, the percentage change is 2.5%.
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