Question

PART A: Rosie writes the equation 24(mx+n)=3x+17, where m and n are real numbers.

Answer 1

Answer:

part A has no solution

part B, I not sure

Answer 2

Answer:

PART A:

$24(mx + n) = 3x + 17$

when m is 14 and n is 13:

$24 \{(14)x + 13) = 3x + 17 \\ 24(14x + 13) = 3x + 17 \\ 336x + 312 = 3x + 17$

collect like terms:

$336x - 3x = 17 - 312 \\ 333x = - 295 \\ x = - 0.886 \\ \\ { \boxed{ \boxed{ \sf{it \: has \: one \: solution}}}}$

PART B:

$if \: m \: is \: 18 \\ 24(18x + n) = 3x + 17$

remember x is -0.886

$24 \{(18 \times - 0.886) + n \} = (3 \times - 0.886) + 17 \\ - 382.752 + 24n = - 26.58 \\ 24n = 356.172 \\ { \boxed{ \boxed{ \sf{n \: is \: 14.8}}}}$