Answer :
So,
We can re-write these statements in mathematical form.
Let h represent Holly and j represent Julia.
First equation: [tex]h + j = 107[/tex]
Second equation: [tex]h = 35 + \frac{1}{2} j[/tex]
This is our System of Simultaneous Linear Equations.
I'll solve.
Substitute
[tex](35 + \frac{1}{2} j) + j = 107[/tex]
Collect Like Terms
[tex]35 + \frac{3}{2} j = 107[/tex]
Subtract 35 from both sides
[tex] \frac{3}{2} j = 72[/tex]
Multiply both sides by [tex] \frac{2}{3} [/tex]
j = 48
Substitute 48 for j in the first equation
h + 48 = 107
Subtract 48 from both sides
h = 59
Check
59 + 48 = 107
107 = 107 This checks.
59 = 35 + [tex] \frac{1}{2} (48)[/tex]
59 = 35 + 24
59 = 59 This also checks.
Holly scored 59 points and Julia scored 48 points.
We can re-write these statements in mathematical form.
Let h represent Holly and j represent Julia.
First equation: [tex]h + j = 107[/tex]
Second equation: [tex]h = 35 + \frac{1}{2} j[/tex]
This is our System of Simultaneous Linear Equations.
I'll solve.
Substitute
[tex](35 + \frac{1}{2} j) + j = 107[/tex]
Collect Like Terms
[tex]35 + \frac{3}{2} j = 107[/tex]
Subtract 35 from both sides
[tex] \frac{3}{2} j = 72[/tex]
Multiply both sides by [tex] \frac{2}{3} [/tex]
j = 48
Substitute 48 for j in the first equation
h + 48 = 107
Subtract 48 from both sides
h = 59
Check
59 + 48 = 107
107 = 107 This checks.
59 = 35 + [tex] \frac{1}{2} (48)[/tex]
59 = 35 + 24
59 = 59 This also checks.
Holly scored 59 points and Julia scored 48 points.
