i do not understand this problem?

Question

1. Paul is fives times as old as his daughter Anna. In 12 years, Paul will be three times as old as Anna is in 12 years. How old is each one now?
2. the sum of three consecutive integers is 444. What are the numbers?

Answer 1

Hi,

Let x = Anna's age. Then if Paul is 5 times as old, then his age now is 5x.

In 12 years, Anna's age will be x + 12 and Paul's age will be 5x + 12. At that time Paul is 3 times as old as Anna, so the equation is Paul's age in 12 years = 3(Anna's age in 12 years).

5x + 12 = 3(x + 12)
5x + 12 = 3x + 36
2x + 12 = 36
2x = 24
x = 12, so Anna's age now is 12 years. that means Paul's age now, 5x, is 60 years old. <== Answer

In 12 years Anna's age would be 24 and Paul's age would be 72, which is exactly 3 times as much as Anna's age, so you can see this answer is correct.


3 consecutive integers can be represented as x for the smallest integer, followed by x + 1 and x + 2. Their sum would be:

x + x+1 + x+2 = 444
3x + 3 = 444
3x = 441
x = 147
So x + 1 = 148 and x + 2 = 149

The numbers are 147, 148, and 149. <== Answer

I hope that helps!! :-)

Answer 2

Let P be the age of Paul and A be the age of Anna (right now).

"Paul is fives times as old as his daughter Anna."

P = 5 A

"In 12 years, Paul will be three times as old as Anna is in 12 years."

P + 12 = 3 ( A + 12 )

Now substitute the expression for P in the first equation into the second...

5 A + 12 = 3 ( A + 12 )
5A + 12 = 3A + 36
2A = 24
A = 12

So Ann is 12 and Paul is 60. 60 is 5 x 12.
In twelve years, Ann will be 24 and Paul 72; 72 = 3 x 24.

Now to the next problem; the sum of three consecutive digits is 444.

D + ( D + 1 ) + ( D + 2 ) = 444
3D = 441
D = 147

The three digits are 147, 148, and 149.

Answer 3

Suppose Anna = x
So, Paul = 5x
After 12 years:
5x + 12 = 3(x + 12)
5x - 3x = 36 - 12
2x = 24
x = 12,
So Anna is12 yrs old and Paul is 5x12=60 yrs old


2. Suppose the no. be x
So,
x + (x + 1) + (x + 2) = 444
3x + 3 = 444
3x = 444 - 3 = 441
x = 441/3 = 147
so the consecutive nos will be.
x = 147, x+1 = 148, x+2 = 149
Adding all three Nos. we get 147+148+149 = 444

Answer 4

x = Anna's age
5x = Paul's age
5x+12 = 3(x+12)
5x+12=3x+36
2x = 24
x = 12 = Anna's age
5x = 60 = Paul's age

3x+3 = 444
3x = 441
x = 147
X=1 = 148
x+2 = 149

Answer 5

1.
Anna: x
Paul: 5x

5x + 12 = 3(x + 12)

Today: Anna 12, Paul 60

2. x + (x + 1) + (x + 2) = 444

147, 148,149