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