There are two numbers whose sum is 53. three times the smaller number is equal to 19 more than the larger number. what are the numbers?

18 and 35. The numbers whose sum 53 are 18 and 35.

The key to solve this problem is using a system of equations.

There are two numbers whose sum is 53. This number can be represented as x and y. So:

x + y = 53

Three times the smaller number is equal to 19 more than the larger. Let's set x as the smaller number and y the larger number. So:

3x = 19 + y

Clear y in both equations and let's use the equalization method to solve for x:

y = 53 - x and y = 3x - 19

Then,

53 - x = 3x - 19

53 + 19 = 3x + x > 3x + x = 53 + 19 > 4x = 72

x = 72/4 = 18

To find y, let's substitute x = 18 in the equation x + y = 53

18 + y = 53 > y = 53 - 18

y = 35

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."