F.1 Maths

Question 1

Let x be the number of $2 stamps
Let y be the number of $5 stamps
x + y = 15 ....... (1)
2x + 5y = 54 ....... (2)

(1) x 2 :
2x + 2y = 30 ....... (3)

(2) - (3) :
3y = 24
y = 8

Put y = 8 into (1)
x + 8 = 15
x = 7

Therefore She buys 7 $2 stamps and 8 $5 stamps.

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Question 2
a) Let x be the number of years time
12 + x = (63+x) / 4
48 + 4x = 63 + x
3x = 15
x = 5
Therefore : After 5 years will Peter's age be a 1/4 of his grandfather age

b) Let y be the number of years time
18 * (12 - y) = 63 - y
216 - 18y = 63 -y
17y = 153
y = 9
Therefore : 9 Years ago was grandfather's age 18 times Peter's

1. Let x be the number of $2 stamps and y be the number of $5 stamps
thus, $2x + $5y = $54 and x + y = 15
then substitute y = 15 - x into $2x + $5y = $54
$2x + $5(15 - x) = $54
$2x + $75 - $5x = $54
$3x = $21
x = 7
i.e. Donna has 7 $2 stamps and 8 $5 stamps

2. what's the meaning of &#39

Donna buys some $2 stamps and some $5 stamps.
If she spends $54 altogether and gets 15 stamps,how many $2 stamps does
she buy?

Ans:
let x be the no. of $2 stamps and y be the no. of $5 stamps
x+y=15................(1)
2x+5y=54............(2)

as x+y=15 then y=15-x

sub y=15-x into (2)
2x + 5(15-x) =54
2x +75 - 5x = 54
-3x = -21
x=7
she buys 7 $2 stamps

Peter is 12 years old and his grandfather is 63 years old now.
a) After how many years" time will Peter age be 四分之一 of his grandfather age ?
b) How many years ago was grandfather's age 18 times Peter's ?

Ans:
(a) let x be the no. of years
(12+x) = 1/4 (63+x)
[ (12+x) is peter's age after x years and (63+x) is grandfather age after x years ]
48 + 4x = 63 +x
3x = 15
x = 5
5 years later

(b) let y be the no. of years
(12-y) = 1/18 (63 - y)
[ (12-y) is peter age y years ago and (63-y) is grandfather age y years ago ]
216 - 18y = 63 - y
153 = 17y
y = 9
9 years ago

Part One:

Assume Donna buys X number of $2 stamps and Y number of $5 stamps.

(1) X+ Y = 15
(2) 2*X + 5*Y = 54

from (1): Y = 15-X ..... (3)
substitute (3) into (2): 2*X + 5 (15-X) = 54
2X + 75 - 5X = 54
-3X = -21
X = 7 ................ (4)

input (4) into (3): Y = 15-7 = 8

Answer: Donna has bought seven $2 stamps and eight $5 stamps.


Part Two:

(a) Assume after X years, Peter's age will be 1/4 of grandfather's age

So: (12 + X) / (63 + X) = 1/4
(12 + X) * 4 = 63 + X
48 + 4X = 63 +X
4X - X = 63 - 48
3X = 15
X = 5

After 5 years, Peter will be 17 and grandfather will be 68 (check: 17 * 4 = 68)

(b) Assume Y years before, grandfather's age was 18 times of Peter's

So: (12 - Y)* 18 = 63- Y
216 - 18Y = 63 - Y
216 - 63 = -Y + 18Y
17 Y = 153
Y = 9

9 years ago, Peter was 3 and grandfather was 54 (check: 3 * 18 = 54)

Let the number of $2 stamp be x and that of $5 stamp be y

2x + 5y = 54 .............(1)
x + y = 15..................(2)

(1) - (2)x2

2x + 5y - 2x - 2y = 54 - 30
3y = 24
y = 8

x = 15 - 8 = 7

So, Donna shall buy 7 $2 stamps


a)
Let the number of years after be A

12 + A = (63 + A)/4
4(12 +A) = 63 + A
48 + 4A = 63 + A
4A - A = 63 - 48
3A = 15
A = 5

Ans.: 5 years after

b)Let the number of years ago be B
63 - B = (12 - B) x 18
63 - B = 216 - 18B
18B - B = 216 - 63
17B = 153
B = 9

Ans.: 9 years ago

Let x be the no. of $2 stamps;
y be the no. of $5 stamps.

--> 2x+5y= 54 (a)

--> x+y= 15 (b)

From (b)
x= 15-y

Put (b) into (a),

2(15-y) + 5y = 54
30 - 2y + 5y = 54
3y = 24
y = 8
--> x= 15-8 = 7
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Let xbe number of $2 stamps bought
then number of $5 bought is15-x

2x+5(15-x)=54
2x+75-5x=54
-3x=-21
x=7

so number of $2 stamps bought is 7

a.let x be the yrs needed

12+x=1/4(63+x)
48+4x=63+x
3x=15
x=5

b.let x be the yrs ago

63-x=18(12-x)
=216-18x
17x=153
x=9