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Peter delivered 210 food orders in a week. For every order that was delivered on time, he earned $3.50. For every order that was delivered late, he would not earn any money and would have to pay a fine of $4.30 instead. He received $532.20 at the end of the week. How many orders were delivered on time?

 Sep 11, 2023
 #1
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Let the number of orders that were delivered on time be \(a\).

 

\(3.5a - 4.3(210-a) = 532.2\)

  \(3.5a-903+4.3a=532.2\)

     \(7.8a-903=532.2\)

          \(7.8a=1435.2\)

               \(a=184\)

 

Now we should check our answers:

 

If \(184\) orders were delivered on time, Peter would have

 

\(184\times$3.5=$644\).

 

If there were \(184\) orders that were on time, there were 

 

\(210-184=26\) late orders.

 

We should now subtract 

 

\(26\times$4.3=$111.8\)

 

from Peter's \($644\).

 

\($644-$111.8=$532.2\)

 

\(184 \) orders were delivered on time.

 Sep 12, 2023

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