Question 1173010
<pre>
Ikleyn below solved the problem using one unknown.  I solve it below using
two unknowns. Both ways are equally correct and give the same answers.

As a rule, using 1 unknown is usually SHORTER, but using 2 unknowns is EASIER
to set up.  So often it is a "give-and-take" situation.</pre>
Bianca and her father picked 109 apples. 
<pre>
Bianca picked x apples.
Her father picked y apples. So,

x + y = 109</pre>Bianca's father picked 13 more apples than triple the apples Bianca picked.<pre>So,

y = 3x + 13

The system of equations to solve is

{{{system(x+y=109,y=3x+13)}}}

Substituting (3x+13) for y in the first equation:

{{{x+(3x+13)=109}}}

{{{x+3x+13=109}}}

{{{4x+13=109}}}

{{{4x=96}}}

{{{x=24}}}   <--so Bianca picked 24 apples

Substitute 24 for x in y=3x+13

{{{y=3(24)+13}}}

{{{y=85}}}   <--so Bianca's father picked 85 apples.

Edwin</pre>