Answer:
c. 21, 85
Step-by-step explanation:
Define the variables:
Let the two numbers be x and y, where x > y.
Given information:
- The larger of two numbers is one more than four times the smaller number.
- The sum of the number is 106.
Create two equations from the given information and defined variables:
[tex]\begin{cases}x = 4y + 1\\x + y = 106\end{cases}[/tex]
Substitute Equation 1 into Equation 2 and solve for y:
[tex]\implies (4y+1)+y=106[/tex]
[tex]\implies 4y+1+y=106[/tex]
[tex]\implies 5y+1=106[/tex]
[tex]\implies 5y+1-1=106-1[/tex]
[tex]\implies 5y=105[/tex]
[tex]\implies \dfrac{5y}{5}=\dfrac{105}{5}[/tex]
[tex]\implies y=21[/tex]
Substitute the found value of y into the second equation and solve for x:
[tex]\implies x+21=106[/tex]
[tex]\implies x+21-21=106-21[/tex]
[tex]\implies x=85[/tex]
Therefore, the two numbers are 21 and 85.
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