What is the minimum number of bracelets that Tessa made last week?

Question

Tessa makes bracelets. She works five days each week, from Monday to Friday. Her contract
requires her to make a minimum of 150 bracelets every working day, for which she is paid a
basic wage of $320 per week. She can also earn a bonus of $3 per bracelet for every one above
175 that she makes on any particular day.
Last week, Tessa earned $515 in total. On Friday she made 205 bracelets, the most she has
ever made in one day.
What is the minimum number of bracelets that Tessa made last week?

Answer 1

The minimum number of bracelets for the week will occur when she makes all of the remaining $3 extra bracelets on one day, since she has a terribly unfair "donut hole" from 150, the minimum per day, and 175, the point where she gets paid more.

 

So, I said:

 

Day 1 = 150,

Day 2 = 150,

Day 3 = 150,

Day 4 = 150 + 25 + 35

Day 5 = 150 + 25 + 30

 

Here's why:  On day 5 she made 205 bracelets.  205 - 150(the minimum) - 25(the donut hole) - 20 = 0.  So, she earned 30 x 3 = 90 dollars extra on day 5.  

 

She earned 515 for the week.  So, 515 - 320(her base rate) - 90 = 105 ( the amount she made on extra bracelets for the whole week.

 

So, 105/3 = 35 extra bracelets, all on day 4.

 

So, 

 

5(150) + 2(25) + 35 + 30 = 865 bracelets

Answer 2

If Tessa made 150 each day, she earns $320 for the week

 

If she makes over 175 in one day, she earns $3 for each one over 175

 

The extra she earned last week = $515 - $320 = $195

 

so $195 ÷ $3 = 65

 

she made 65 bracelets over 175 last week

 

If she made 205 on Friday, that's 30 over 175 

 

65 extras - 30 extras on Friday = 35 extras another day

 

She made another 35 bracelets over 175 another day

 

175 + 35 = 210 bracelets

 

To get a minimum made for the week, assume she made 150 on the other 3 days

 

150 + 150 + 150 + 210 + 205 = 865

 

She had to have made at least 865 last week

 

On any of the other three days , she could have made some number between 150 and 175 and earned no extra money 

 

but this would not be the minimum number you're looking for.