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, 2025

Algebra Difficulty 2.0 Junior Prove it Canada

To begin, tokens are distributed unequally between two
people. Every minute following this, each person receives $2$ more tokens.

Tokens are distributed between Abi and
Brody with Abi receiving $30$ tokens
and Brody receiving $10$ tokens. How
many tokens does Abi have in total after $7$ minutes?
A total of $80$ tokens are distributed between Carl
and Desiree. After $12$ minutes,
Desiree has $37$ tokens. How many
tokens did Carl start with?
A total of $100$ tokens are distributed between Essi
and Francis, with Essi receiving $12$
tokens. After $t$ minutes, Francis
has $3$ times as many tokens as Essi.
Determine the value of $t$ .

Solution

After $7$ minutes, Abi has a
total of $30+(7\times2)=30+14=44$
tokens.
After $12$ minutes, Desiree
had received $12\times2=24$
additional tokens. After $12$
minutes, she had $37$ tokens in
total, and so Desiree started with $37-24=13$ tokens.

A total of $80$ tokens were initially
distributed, and so Carl started with $80-13=67$ tokens.
At the start, Essi received $12$ tokens and Francis received $100-12=88$ tokens.

After $t$ minutes, Essi has $12+2t$ tokens and Francis has $88+2t$ tokens.

After $t$ minutes, Francis has $3$ times as many tokens as Essi, and so
$88+2t=3(12+2t)$ . Solving for $t$ , we get $88+2t=36+6t$ or $52=4t$ , and so $t=\dfrac{52}{4}=13$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.