Respuesta :
Let the larger number be
[tex]=x[/tex]Let the smaller number be
[tex]=y[/tex]Step 1: Represent the expression below as an equation
The larger of two numbers is 18 more than 5 times the smaller
[tex]\begin{gathered} \text{Five times the smaller number } \\ =5\times y \\ =5y \\ 18\text{ more than 5 times the smaller number will be} \\ x=5y+18\ldots\ldots\ldots\text{.(equation 1)} \end{gathered}[/tex]Step 2: Represent the expression below as an equation
3 times the larger number is increased by 4 times the smaller, the result is 16.
[tex]\begin{gathered} 3\text{ times the larger number will be} \\ =3\times x \\ =3x \\ 4\text{ times the smaller number will be} \\ =4\times y \\ =4y \\ \text{Therefore, the equation will be} \\ 3x+4y=16\ldots\ldots\ldots\text{.(equation 2)} \end{gathered}[/tex]The positive sign was used in equation 2 because the question said increased
Step 3: Substitute equation (1) in equation (2)
[tex]\begin{gathered} 3x+4y=16\ldots\ldots\ldots\text{.(equation 2)} \\ x=5y+18\ldots\text{.}(\text{equation 1)} \\ \text{hence,we will have} \\ 3(5y+18)+4y=16 \\ \text{expnading the brackets, we will have} \\ 15y+54+4y=16 \\ \text{collect similar terms,} \\ 15y+4y+54=16 \\ 19y+54=16 \end{gathered}[/tex]Step 4: subtract 54 from both sides
[tex]\begin{gathered} 19y+54=16 \\ 19y+54-54=16-54 \\ 19y=-38 \\ \text{divide both sides by 19} \\ \frac{19y}{19}=-\frac{38}{-19} \\ y=-2 \end{gathered}[/tex]Step 5: Substitute the value of y=-2 in equation (1) to get the value of x
[tex]\begin{gathered} x=5y+18 \\ x=5(-2)+18 \\ x=-10+18 \\ x=8 \end{gathered}[/tex]Hence,
The larger number is = 8
The smaller number = -2
