# F.3 Maths

1.The length of a neck-tie shrinks by 4% after each wash. If the original length of the neck-tie is 120cm, find the percentage change in the length of the neck-tie after 3 washes. (Give your answer correct to 1 decimal place.)

2. The price of a new device is \$750. Its price increases at a rate of 5% per week for the first three weeks after issue, and then decreases at a rate of 9% per week for the following two weeks. Find the price of the device after 5 weeks of its issue. (GIVE YOUR ANSWER CORRECT TO THE NEAREST \$1)

question 2, I do not know which step i did wrong, i always find out the answeris 720, the right answer is 719.

### 1 個解答

• 7 年前
最愛解答

smile, please also understand the method of the calculation rather than using our answers directly.

1.

After 3 washes, the length becomes 120*(1-4%)*(1-4%)*(1-4%) = 106.16832 cm

The percentage change in length is

(106.16832-120)/120*100% = -11.5264% = -11.5% (cor to 1 d.p.)

2.

The price of the device after 5 weeks is

\$750*(1+5%)*(1+5%)*(1+5%)*(1-9%)*(1-9%) = \$718.971946875 = \$719 (cor nearest \$1)

2013-07-25 18:05:35 補充：

你說你計過幾次都係計到720，咁有可能係你唔係一次過計到尾，而係你分段咁計，而每步你都round左，有rounding error。

例如：

\$750*(1+5%)=\$787.5 round to \$788

\$788*(1+5%)=\$827.4 round to \$827

\$827*(1+5%)=\$868.35 round to \$868

\$868*(1-9%)=\$789.88 round to \$790

等等

如果咁計，你有可能會累積ｄ rounding error，要留意呢點。

資料來源： Calculated