please answer?

Question

1)three times the greatest of three even integers exceeds twice the least by 38. find the integers.

2)the difference of two numbers is 12. two fifths of the greater number is six more than one third of the lesser number. find both numbers.


could you write the equation, define a variable, as well as the answer. i'm sorry this is how i understand problems.

Answer 1

I think that it is 1 and 2. Go with that

Answer 2

1) let a, b, c be three even integers
where a < b < c
3c = 2a + 38
3c - 2a = 38
where n is an even integer
c = 38 + 2n >= 0 ==> n >= - 19
a = 38 - 3n >= 0 ==> n <= 38/3 = 12.666666667
so -19 < n <= 12, n = {-18, -16, ... , 0, 1, 2,... 11, 12}

2) let a and b be two numbers (a>b)
a - b = 12
(2/5) a = (1/3) b + 6

a - b = 12
(2/5) a - (1/3)b = 6

a - b = 12
6a - 5b = 12 *15 = 180

a - b = 12
0 -5b + 6b = 180 - 6*12
b= 108
a = 120

Answer 3

1) This question has infinite answers, because there's not enough information to find a unique answer. Perhaps you're missing something in the question?


2) Let the lesser number be x.
Then the greater number must be x + 12, since x - (x + 12) = 12

Two fifths of the greater number is six more than one third of the lesser number, which gives us the equation:

(2/5)*(x + 12) = (1/3)*x + 6
2x/5 + 24/5 = x/3 + 6
2x/5 - x/3 = 6 - 24/5
6x/15 - 5x/15 = 30/5 - 24/5
x/15 = 6/5
x = 90/5 = 18

Therefore, the lesser number is 18, and the greater number is 18 + 12 = 30.

Answer 4

1. You are missing something here.
2. Let B be the bigger number, A the smaller number.
Math statement 1 B-A=12
Math statement 2 2/5 B = 1/3 A +6
(the solution is B=30, A= 18)

Answer 5

3 times 38 equals 114

Answer 6

2.
x and x+12

2(x+12)/5 = 1(x)/3 + 6
(2x+24)/5 = x/3 + 6
2x+24 = 5(x/3 + 6)
2x+24 = 5x/3 + 30
2x-(5x/3) = 30-24
(6x-5x)/3 = 6
x/3 =6
x = (6)(3)
x = 18
x+12 = 30
18 and 30
check:
30-18=12
2/5 of 30 is 12
1/3 of 18 is 6
(12) = 6 + (6)

Answer 7

x-y=12
2/5x+6=2/3y