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