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Algebra Difficulty 1.0 Junior Prove it Canada

Azizi sold chocolate bars from Monday to Friday over three
weeks.

During the first week, he sold the
following numbers of chocolate bars:

Monday
Tuesday
Wednesday
Thursday
Friday

$15$ $23$ $18$ $15$ $7$ How many chocolate bars did he sell in total during the first week? During the second week, he sold the following numbers of chocolate bars: Monday Tuesday Wednesday Thursday Friday $7$ $15$ $x$ $23$ $x$ He sold a total of $73$ chocolate bars during the second week. What is the value of $x$ ? During the third week, he sold $y$ chocolate bars on Monday. Each day from Tuesday to Friday, he sold $6$ more chocolate bars than he sold on the previous day. He sold a total of $100$ chocolate bars during the third week. Determine the value of $y$ .

Solution

During the first week, Azizi sold a total of $15+23+18+15+7=78$ chocolate bars. During the second week, Azizi sold a total of $7+15+x+23+x=45+2x$ chocolate bars, and so $45+2x=73$ . Solving $45+2x=73$ , we get $2x=28$ , and so $x=14$ . During the third week, Azizi sold $y$ chocolate bars on Monday, $y+6$ on Tuesday, $y+12$ on Wednesday, $y+18$ on Thursday, and $y+24$ on Friday. In total, he sold $y+(y+6)+(y+12)+(y+18)+(y+24)=5y+60$ chocolate bars, and so $5y+60=100$ . Solving $5y+60=100$ , we get $5y=40$ , and so $y=8$ . (Can you explain why the total number sold, $5y+60$ , is equal to $5$ times the number that Azizi sold on
Wednesday?)

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