Q&A - PSLE Math

[wahwah]

Hi,

Need some urgent help with the following math questions.

Mary spent 3/7 of her money on 6 marbles and 6 crystal balls and 1/4 of the remainder on 10 metal balls. Each marble cost 1/7 as much as a crystal ball. Each metal ball cost $0.90 more than a marble. How much money did Mary have at first?

The bookshelves in a library were arranged in rows of 8 shelves each.
The library bought another 4 shelves and rearranged the shelves into rows of 6 shelves each. After the rearrangement, the librarian found that he had 10 additional rows of shelves. How many shelves were there in the library in the end?

Many thanks in advance.

[MathIzzzFun]

wahwah:

Hi,

Need some urgent help with the following math questions.

Mary spent 3/7 of her money on 6 marbles and 6 crystal balls and 1/4 of the remainder on 10 metal balls. Each marble cost 1/7 as much as a crystal ball. Each metal ball cost $0.90 more than a marble. How much money did Mary have at first?

Cost of 1 marble --> 1 unit
Cost of 1 crystal ball --> 7 units

3/7 of money --> 6 units + 42 units = 48 units
1/7 of money --> 16 units, Total amount of money --> 112 units

Cost of 10 metal balls --> 1/4 of remainder = 1/4 x 4/7 of money = 1/7 of money
so, cost of 10 metal balls --> 16 units,
cost of 1 metal ball --> 1.6 units

1 metal ball cost $0.90 more than 1 marble
so, 0.6 unit --> $0.90
1 unit --> $1.50

Total amount of money --> 112 x $ 1.50 = $ 168

cheers.

[MathIzzzFun]

wahwah:

Hi,

Need some urgent help with the following math questions.

The bookshelves in a library were arranged in rows of 8 shelves each.
The library bought another 4 shelves and rearranged the shelves into rows of 6 shelves each. After the rearrangement, the librarian found that he had 10 additional rows of shelves. How many shelves were there in the library in the end?

Many thanks in advance.

10 additional rows of shelves --> 10 x 6 = 60 shelves
Total number of shelves removed from original number of rows (2 were removed from each row) = 60 - 4 = 56

At first, number of rows of shelves = 56/2 = 28

In the end, total number of shelves = 28 x 8 + 4 = 228

cheers.

[MathIzzzFun]

iamproudparents:

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James and Bond had $728 altogether. When James spent 1/4 of his money and Bond spend 2/3 of his, they found out that each had an equal amount of money left. How much did James have at first ?

Equal fraction/numerator method

http://www.tinyurl.com/mathizzzfun-equalfractions

Amount left :
3/4 James' money = 1/3 Bond's money
3/4 James' money = 3/9 Bond's money

James' money --> 4 units
Bond's money --> 9 units
Total --> 13 units --- $728
1 unit --> $56

Jame's money --> 4 x $56 = $224

cheers.

[wahwah]

MathIzzzFun,

Thanks so much!

[MathIzzzFun]

iamproudparents:

http://i46.tinypic.com/35hr769.jpg\">

Cross-multiply/UP (units-parts) method:

At first, John's money : Daisy's money --> 1 unit : 8 units
In the end, John's money : Daisy's money
-> 1 unit - $80 : 8 units - $985
= 3 : 1 (or 3 parts : 1 part)

Cross-multiply / Equalize parts:

1 unit - $80 = 24 units - $2955
1 unit --> $125

John's money, at first --> $ 125


cheers.

[MathIzzzFun]

iamproudparents:

http://i48.tinypic.com/2usex3d.jpg\">

by train --> 7/10 tour = 14/20 tour
by coach --> 1/4 tour = 5/20 tour

1 - 14/20 - 5/20 = 1/20

by car --> 1/20 tour

14/20 - 1/20 = 13/20

13/20 tour --> 416 km
tour --> 416 km/13 x 20 = 640 km

total distance pf the tour = 640 km

cheers.

[MathIzzzFun]

iamproudparents:

http://i48.tinypic.com/5a8w1.jpg\">

$0.90 = $0.50 + 2 x $0.20 --> 1 x 50-cent + 2 x 20-cent
Total amount left = $16.20 - $0.90 = $15.30

1 set of (3 x 50-cent coin + 1 x 20-cent coins) = $1.50 + $0.20 = $1.70
Number of sets = $ 15.30 / $ 1.70 = 9

At first,
number of 20-cent coins --> 9 + 2 = 11
number of 50-cent coins --> 9 x 3 + 1 = 28

cheers.

[MathIzzzFun]

iamproudparents:

http://i47.tinypic.com/3442yxz.jpg\">

a) 30 dots used, number of dots per side = 30/5 + 1 = 7
or (30+5)/5 = 7

b) 47 dots per side, total --> (47-1) x 5 = 230
or 47 x 5 - 5 = 230

cheers.

[MathIzzzFun]

iamproudparents:

http://i46.tinypic.com/2zyzul5.jpg\">

a)
total number = sum of squares
pattern 1 = 1² = 1
pattern 2 = 1² + 2² = 5
pattern 6 = 1² + 2² + 3² + 4² + 5² + 6² = 91

b)
total number of cubes = 27 405 / 27 = 1015
use the calculator and add the squares to 1015

pattern 14 = 1² + 2² + 3² + 4² ......+ 13² + 14² = 1015

(* shortcut : number of cubes in pattern N = N(N+1)(2N+1)/6 )

cheers.