Word problems?

Question

need some help

>the middle digit of a three digit number is 3 more that twice the extreme digits which are numerically equal. if the number is divided by 3 the number formed is 11 more than 8 times the sum of the digits. Find the number

Answer 1

make abc be the 3 digit number.
a=c
b = 2a +3
(100a +10b +c)/3 = 8 (a +b +c) +11
Now just start substituting
(100a + 10b +a)/3 = 8 (a +b +a) +11
100a + 10b + a = 24a +24b + 24 a + 33
53a = 14b +33
Substitute again
53a = 14(2a +3) +33
25a = 75
a = 3 and c = 3
b = 2a + 3 so b = 9
The number is 393

Answer 2

Number is aba

the middle digit of a three digit number is 3 more that twice the extreme digits which are numerically equal

Not sure what this means - it could be

b = 2a + 3

if so, it should have said 3 more than twice either extreme digit, which are numerically equal

f the number is divided by 3 the number formed is 11 more than 8 times the sum of the digits.

(100a + 10b + a)/3 = 8(a + b + a) + 11
(101a + 10b)/3 = 8(2a + b) + 11
101a + 10b = 24(2a + b) + 11
101a + 10b = 48a + 24b + 11
53a - 14b = 11

53a - 14(2a + 3) = 11
53a - 28a - 42 = 11
25a = 53

So I guess I don't grok the first statement!

Answer 3

Ok.
So, we have a 3 digit number.
xyz
The middle digit of the three digit number is 3 more than twice the extreme digits, which are numerically equal.

Since the extreme digits are numerically equal, this means:
x = z

So, our 3 digit number can be written
xyx

Now, since the middle number is 3 more than twice the extreme digits, this means:
2x + 3 = y.


We are also told that if the number is divided by 3, the number formed is 11 more than 8 times the sum of the digits. This means
(xyx) / 3 = 11 + 8(x + y + x)
If we multiply both sides by 3 we have
xyx = 33 + 24(x + y + x)

We know y = 2x + 3, so plug that in:

x(2x+3)x = 33 + 24(x + (2x+3) + x)
= 96x + 105

Now, this is where it gets cool.
Divide both sides by 100. Since it is a 3 digit number x(2x+3)x, when we divide by 100 we have x . (2x+3)x

x. (2x +3)x = (96x + 105) / (100)
Subtract x from both sides.

. (2x + 3)x = (96x + 105) / 100 - x
Now multiply by 10. Since we have . (2x +3)x, when we multiply by 10 it becomes (2x + 3) . x

(2x + 3) . x = (96x + 105) / 10 - 10x
Subtract (2x + 3) from both sides.

. x = (96x + 105) / 10 - 10 x - (2x + 3)
- (2x + 3) = -2x - 3 So we have:
. x = (96x + 105) / 10 - 10x - 2x - 3

Now multiply both sides by 10. Since it is . x, when we multiply by 10, it becomes x

x = 96x + 105 - 100x - 20x - 30
Simplifying we have
x = -24x + 75
Add 24x to both sides
25 x = 75
Divide both sides by 25

x = 3

Now, plug this into our original equation that said 2x + 3 = y

2(3) + 3 = y
6 + 3 = y

y = 9

So, our number is

393

Answer 4

answer is 393.

lets suppose,1st digit=x, 2nd digit=y and 3rd digit=z

According to question, x=z then the three digit number is
100x+10y+x ie. 101x+10y

1st equation is, y=3+2x

2nd equation is, (101x+10y)1/3=11+8(2x+y)
ie. 101x+10y=33+24(2x+y)

now put the value of y in terms of x from equation one.Then solve for x.Value of x is 3.if x=3 , y=9 which means the three digit number we require is 393.

Hope u got it.

Answer 5

xyx be the number.
x+10y+100x=number
y=2x+3 --- (1)
(101x+10y)/3=8(2x+y)+11
101x+10y=24(2x+y)+11
101x+10y=48x+24y+11
53x-14y=11
using (1)
53x-14(2x+3)=11
53x-28x-42=11
25x=53
I must have done something wrong?