Can you help me to do this math question(my homework)?

Question

Here is the question:
1) A father three times as old as his son. In 12 years' time, he will be twice as old as his son. How old is the father now?
2) When Mrs Joseph bought five apples and three pears, she recknocked that she would have to pay 80 cents more if she had bought three apples and five pears. What was the difference beetwen the price of one pear and the price of one apple?

Answer 1

3x=father x=son

3x=2x+12
x=12
father is 36, in 12 years he will be 48, son 24

5a+3p=3a+5p+80 sub 3p from both sides
5a=3a+2p+80 sub 3a from both sides
2a=2p+80 divide by 2
a=p+40
apple is 40 cents more than pear

http://www.khake.com/page47
"How To Solve It" by G. Polya

Answer 2

1) Let x = son's age now
and 3x = father's age now

Then x + 12 = son's age in 12 years and
3x + 12 = father's age in 12 years

Since the father will be twice as old as the son in 12 years, you get

3x + 12 = 2(x + 12)

3x + 12 = 2x + 24

x = 12 yrs = son's age now
3x = 36 yrs = father's age now

Check: in 12 years the son will be 24 and the father will be 48 which makes the father twice as old as the son.

2) Let p = price of one pear and a = price of one apple

Then the total price of 5 apples and 3 pears is 5a + 3p.
Also the total price of 3 apples and 5 pears is 3a + 5p.

Since the 1st case is 80 cents more than the second case, you get

5a + 3p = 3a + 5p + 80

2a - 2p = 80

a - p = 40

Therefore, the difference between the price of one pear and one apple is 40 cents

Answer 3

1) Let the sons present age be x years.So the fathers present age is 3x years. kTherefore according to the problem 3x+12= 2(x+12) => 3x+12 = 2x+24 => 3x-2x = 24 - 12 =12 yrs Therefore,the present age of the father is 12X3=36 years 2) Let ,the cost of an apple be x cents and that of a pear be y cents .Therefore,the cost of five apples and three pears is 5x+3y and the cost of three apples and five pears would be 3x +5y Now,according to the problem 3x+5y =5x+3y+80 => 5y-3y=5x-3x +80 => 2y=2x +80 => y=x+40 .Therefore,the cost of a pear is 40 cents more than that of an apple,

Answer 4

didn't figure out the 2nd answer, but the first answer is that the father is 36 yrs old. The son is 12. In 12 years, the son will be 24, and the dad will be 48.

Answer 5

1) x father, y kid
x=3y => y=x/3
(x+12)=2(y+12)=> x + 12=2(x/3+12)=2x/3 + 24 => x - 2x/3 = 12
x/3=12=> 36

2) 5a + 3p = $
3a + 5p = 80 + $ => 3a + 5p -80 = 5a + 3p
2p - 2a = 80
p-a=40 cents

Answer 6

First one is easy.
For the second , let a be the price of an apple , p of pear.Then
5a+3p=x (say)
Also
3a+5p=x+80

Subtract 2nd eq from the 1st
2a-2p=-80
or
p-a=40 cents

Answer 7

1) x=3y
x+12=2[y+12]
or 0 -12 =y - 24 or y =12 ; father is 36
2) 5x+3y=p
3x+5y=p-80
or 2x-2y=80
x-y =40 = price difference

Answer 8

I think hes 63 years old