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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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