Question

The salary of 8 men and 6 women amount to $\$66$. If 5 women earn $\$9$ less than 4 men, determine the salary of each man and woman.

• A. $\$1.50,\$3$
• B. $\$3,\$6$
• C. $\$2.50,\$5$
• D. $\$6,\$3$

Answer 1

The correct option is D $\$6,\$3$

Let the salary of one man be $x$ and that of one woman be $y$, Then
$8x+6y=66$.......(i)
$4x-5y=9$..........(ii)
From equation (i)
$8x+6y=66$
Dividing both sides by 2
$4x+3y=33$........(iii)
Now using the method of elimination, we subtract (ii) from (iii)
$4x+3y=33$
$4x-5y=9$
__________
$8y=24$
$y=3$
Putting value of $y=3$ in equation (ii)
$4x-5\left(3\right)=9$
$4x-15=9$
$4x=9+15$
$4x=24$
$x=6$
Correct option is D