The sum of three numbers is -3. the last number is three times the first. the last number is 11 smaller than the second number. what are the three numbers.

ANSWER:

The value of the three numbers are -2, 5 and -6 respectively.

SOLUTION:

Let us say the unknown numbers 1, 2 and 3 are x, y and z respectively.

It is given to us that the last number is three times the first number.

Therefore, we can write it as;

z = 3x  --- eq1

It is also given that the last number is 11 smaller than the second number.

Which can be written as;

z  = y-11   eq2

we are also given that the sum of all three numbers is -3.

So, we can form the equation as follows;

x + y + z = -3 eq3

By equating equation 1 and equation 2 we get

3x = y – 11

y = 3x + 11 --- equation 4

By substituting eqn 1, 4 into equation 3 we get,

x + 3x + 11 + 3x = -3

7x + 11 = -3

7x = -14

x = -2

By substituting the value of “x” in eqn 1 we get z = -6

By substituting the value of “x” in eqn 4 we get y = -6 +11 = 5

Hence the three numbers are -2, 5 and -6

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