Q&A - PSLE Math

[MathIzzzFun]

Chalupa:

Town A and Town B are 375km apart.Wen set off from Town A towards Town B at 1400 at a constant speed of 60km/h.1h later,Nelly set off from Town B towards Town At a constant speed of 80km/h.At what time did the two girls meet on the road? :thankyou:

1h later at 15:00, the distance between Wen and Nelly
= 375 km - 60 km
= 315 km

In 1h,
total distance travelled by Wen and Nelly = 60 km + 80 km = 140 km
--> the distance (gap) between them reduces by 140 km in 1 hour

Time taken for the distance to reduce to zero --> 315 / 140 = 2.25h = 2h 15min

15:00 + 2h 15 min --> 17:15
they met at 17:15

cheers.

[Chalupa]

Thanks for the solution, but I don’t know how the no. Of apples are 25 units. Can you Please explain.

[PapayaDad]

after he sold 1/5 of his apples…

normally we will start with apple = 5u
sold 1/5 left 4u…

then… the number of oranges was 2/5 the number of apples…
aiya… 2/5 of 4u how ar?

so better go back and make apple = 25u (so i can divide it by 5 twice)
sold 1/5 left 20u
2/5 of 20u = 8u…

[ozora]

http://i40.tinypic.com/4rvu3k.jpg\">

wonder is the answer 65 or 75?

[MathIzzzFun]

Chalupa:

Thanks for the solution, but I don't know how the no. Of apples are 25 units. Can you Please explain.

A fruit seller had 600 apples & oranges altogether. After he sold 1/5 of his apples and bought another 60 oranges, the number of oranges was 2/5 the number of apples. How many more apples than oranges were there at first.

From the question, we see that the number of apples need to be divided by 5 twice
1/5 x1/5 = 1/25 --> so start with Apples --> 25 units

Of course, we can also start with Apples --> 5 units or even Apples --> 1 unit... with these, we will have to work with fractions/decimals.

For eg

at first, apples --> 5 units
after selling 1/5, apples left --> 4 units
number of oranges (after buying another 60) --> 2/5 x 4 units = 1.6 units

at first, number of oranges --> 1.6 units - 60

Total number of apples and oranges at first --> 6.6 units - 60
so, 6.6 units - 60 = 600
6.6 units --> 660
1 unit --> 100

At first,
apples --> 5 x 100 = 500
oranges --> 1.6 x 100 - 60 = 100
there were 400 more apples than oranges at first.

cheers.

[MathIzzzFun]

ozora:

http://i40.tinypic.com/4rvu3k.jpg\">

wonder is the answer 65 or 75?

a=70
b=75
c=40
d=30
e=35
f=45
m=n=65
p=115

cheers.

[ozora]

MathIzzzFun:

ozora:

http://i40.tinypic.com/4rvu3k.jpg\">

wonder is the answer 65 or 75?

a=70
b=75
c=40
d=30
e=35
f=45
m=n=65
p=115

cheers.

thanks. a bit loss for m and b.
could you possible provide start of the working for me to check.
thanks maths

[MathIzzzFun]

lee tong fong:

Hi, can anyone help me with another question


(2) Joey has some red and blue beads.
If she buys another 15 red beads, the percentage of the red beads she has become 30%.--> red : blue = 3 : 7
If she gives away 20 blue beads, the percentage of the blue beads she has becomes 76%.--> red : blue = 24 : 76 = 6 : 19
However many red beads and blue beads do Joey have?

Thanks you again

IF Joey buys another 15 red beads,
red beads : blue beads --> 3u : 7u

AT FIRST, red beads : blue beads --> 3u - 15 : 7u
If she gives away 20 blue beads,
red beads : blue beads
--> 3u -15 : 7u - 20
= 6 : 19

equalize / cross multiply:

57u -285 = 42u -120
1u --> 11

At first,
red beads --> 3 x11 - 15 =18
blue beads --> 7 x 11 = 77

cheers.

[ozora]

Mathizzfun thanks solved

[cimman]

ozora:

http://i40.tinypic.com/4rvu3k.jpg\">

wonder is the answer 65 or 75?

http://i40.tinypic.com/i42046.png\">

this problem is made up of a number of equations, similar to this type of problem sums:
Three boys, Alan, Bernard and Calvin sat for a test. The average score of Alan and Bernard was 78 marks, the average score of Bernard and Calvin was 74 marks and the average score of Alan and Calvin was 80 marks. Find the marks scored by each of them.

The key is to figure out how to combine specific equations together to eliminate some variables. Since this problem is about angles, we need to do some inference on angles before we begin to combine equations together.
In any angle problems, we always look for same angle properties. The key is to look for parallel sides or sides with same lengths (isosceles triangles). However, none of that exists in this diagram. However we do note that n = m.
The other property that we need to take note of, is that the interior angles of a triangle adds up to 180 or the interior angle of a quadrilateral adds up to 360. This property gives us another inference (on equation) that is not normally stated in the figure diagrams.
In this case, we don't have a quadrilateral shape, but we do have triangle shapes.
There are 3 triangles:
a + f + n = 180
p + e + d = 180
m + b + c = 180

so, with the 2 inferences that we have made (m=n, and the equations that gives 180), we can move on to the next step.

amongst all the 4 equations given in the problem sum, a + m = 135 is the most useful to start of with because it can be translated to a + n = 135, since m = n. (a + n) is useful because it gives us part of the equation that will lead us to 180. All we need now, is to link it to f.

We find that equation 4, will give us that variable, f. So, we will start off with adding equation 1 and equation 4, which will utilize our inference that
a + f + n = 180

http://i44.tinypic.com/33mr12o.png\">

there are other combinations to solve this, but the main idea is to make the necessary inferences on angles and interior angles of a triangle, and then look for equations with variables that will utilize the inferences.