Answer : The true statements are:
The equation [tex]c+d=58[/tex] represents the sum of two numbers.
The equation [tex]c=\frac{d}{2}-8[/tex] represents the relationship between the two numbers.
The number c is, 14
The number d is, 44
Step-by-step explanation :
Given:
Let 'c' represent the first number. Let 'd' represent the second number.
The sum of two numbers is 58. The equation will be:
[tex]c+d=58[/tex] .........(1)
The first number is 8 less than half the second number. The equation will be:
[tex]c=\frac{d}{2}-8[/tex] .........(2)
Now by solving the two equations, we get the value of c and d.
As, [tex]c+d=58[/tex]
or, [tex]c=58-d[/tex] ..........(3)
Now put equation 3 in 2, we get the value of d.
[tex]58-d=\frac{d}{2}-8[/tex]
[tex]58-d=\frac{d-16}{2}[/tex]
[tex]2(58-d)=d-16[/tex]
[tex]116-2d=d-16[/tex]
[tex]3d=132[/tex]
[tex]d=44[/tex]
Now put the value of 'd' in equation 3, we get the value of 'c'.
[tex]c=58-d[/tex]
[tex]c=58-44[/tex]
[tex]c=14[/tex]
Thus, the value of c and d is, 14 and 44 respectively.
