Statement Problem: The sum of two numbers is 7. Five times the larger number plus four times the smaller number is 48. Find the numbers.
Solution:
Let x be the larger number and y be the smaller number such that;
[tex]\begin{gathered} x+y=7\ldots.\ldots\ldots\text{equation}1 \\ 5x+4y=48\ldots\ldots\text{.equation}2 \end{gathered}[/tex]From equation 1, we have;
[tex]\begin{gathered} x+y=7 \\ x=7-y\ldots\ldots\ldots....\text{equation}3 \end{gathered}[/tex]Substitute equation3 in equation2, we have;
[tex]\begin{gathered} 5x+4y=48 \\ 5(7-y)+4y=48 \\ 35-5y+4y=48 \\ -1y=48-35 \\ -1y=13 \\ \text{Divide both sides by -1;} \\ -\frac{1y}{-1}=\frac{13}{-1} \\ y=-13 \end{gathered}[/tex]Then, substitute the value of y in equation3;
[tex]\begin{gathered} x=7-y \\ x=7-(-13) \\ x=7+13 \\ x=20 \end{gathered}[/tex]Thus, the larger number is 20 and the smaller number is -13