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 Forum Index >  Test Paper Related >  Primary 6 Matters
 Help needed on 3 maths questions
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By: Kuro (offline)  Friday, June 27 2014 @ 08:57 PM CDT (Read 1209 times)  

Q1. Alice went shopping with a sum of money. She spent all her money in 2 stores. In each store,
she spent $18 more than half of what she had left when she entered the store.
(a) How much did she spend at the second store? Ans. $36
(b) How much money did she have at first? Ans. $108

Q2. At 8.30am, a motorcycle left Town A for Town B travelling at 60km/h.
1/1/2 hour later, a car left Town A travelling at 85km/h.
The car overtook the motorcycle midway between Town A and Town B, and reached Town B first.
What was the distance between Town A & Town B? Ans. 612km

Q3 is in attachment.

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By: jo sarah (offline)  Saturday, June 28 2014 @ 09:53 AM CDT  
jo sarah


let me start with no. 3 (most interesting):

Qn 3:

area of BEC - white unshaded area = shaded area Y
area of ABCD - white unshaded area = shaded area X

notice: there is a common white unshaded area in both cases, which can be removed from the equation.

(1/2) x 9 x 7 - (white unshaded) - 13.5 = 9 x AB - (white unshaded)
63 / 2 - 13.5 = 9 x AB
AB = (31.5 - 13.5) / 9 = 18 / = 2 cm

Qn 1:
(a) in the second store, she spent $18 more than half of what she had left after spending money in first store.
so this $18 is really half of what's left after spending at first store, right?

so, she spent $18 x 2 = $36 at second store.

(b) this $36 + $18 = $54 will then be half of all money she had when she entered 1st store.
thus, she had $54 x 2 = $108 at first, when she went shopping.

Qn 2:
since motorcyclist went ahead of car by 1.5 hours, he was thus 1.5 h x 60 km/h = 90 km ahead of car at 10 am when car left.
now, car needed to catch up that distance of 90 km.
from 10 am, car is ahead in distance of motorcyclist by (85 - 60) km/h = 25 km/h
therefore, car took 90 km / 25 km/h = 18 / 5 hours to catch up and overtook other at mid-point.
that is to say, car travelled total distance of (18/5) h x 85 km/h = 306 km
and this is at mid-point between two towns.
So, total distance between two towns = 306 km x 2 = 612 km


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