Question

In a gymnastics competition, Holly and Julia scored a total of 107 points. Holly scored 35 more points than one half of Julia’s points. Write and solve an equation to determine who scored more points. What is the difference between their scores?

Answer 1

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.