maths! maths! maths!

4.Let the number of $2 be x,then the number of $5 be 60-x.
2x+5(60-x)=195
2x+300-5x=195
-3x=-105
x=35
∴The number of $2 is 35,then the number of $5 is 25.

5.Let the present age of his father be x,then the age of a boy be 1/3x +1.
1/2(x+5)-4 =(1/3x +1 )+5
3(x+5)-24=2x+6+30
3x+15-24=2x+36
3x-9=2x+36
x=45
∴The present age of his father is 45.

6a.
Let the cost of apple and orange be $x and $y.
2x+3y=12____________________(1)
4x+2y=16____________________(2)

Solve (1) and (2),we have
x=3 and y=2
∴Apple and an orange cost $3 and $2.

b.
John should pay=3(3)+4(2)
=$21

4. A bag contains 60 cains which are either $ 2 or $ 5 coins. The total value of the coins is $ 195. Find the number of each type of coins.
suppose there is x $2 coins and y $5 coins
x+y=60-----a
2x+5y=195----b
from a: x=60-y----c
put c into b: 120-2y+5y=195
3y=75
y=25
x=35




5. The age of a boy exceeds one - third of his father' s by 1. Five years later his age will be 4 less than half of his father' s. What is the present age of his father.
let father age now be x
age of boy be y
now,
y=1/3x+1
five years later:
y+5=(x+5)/2-4
y=(x+5)/2-9
1/3x+1=(x+5)/2-9
multiply by 6:
2x+6=3x+15-54
45=x
father now =45
boy now=16





6. Peter, Mary and John went to the supermaket. Peter bought 2 apples and 3 oranges. Mary bought 4 apples and 2 oranges, while John bought 3 apples and 4 oranges. Peter paid $ 12 while Mary paid $ 16.


a. How many did an apple and an orange cost respectively?
let number of apple = x
number of orange be y
2x+3y=12----a
4x+2y=16----b
from b, 2x+y=8
y=8-2x
put in a:
2x+24-6x=12
4x=12
x=3
y=2


b. How much should John pay?
3x+4y
=9+8+17