Isaac makes china mugs with names painted on them. He charges a fixed fee for the mug, together with a fixed charge for each letter in the name. Penelope buys a mug for each of her children, Alexander and Lucia. She pays $12.60 for Alexander’s mug and $9.40 for Lucia’s mug. How much would Penelope have to pay for a mug with her own name on it?

I found how many more letters Alexander had over Lucia, then when I got 4 divided it in-between 12.60 - 9.40 (3.20) I got 0.8. knowing the letter cost i got the initial fee for the mug (5.40) and added 8x0.8 to it, resulting in my answer 11.80$

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ashishdwivedilVT ashishdwivedilVT · Answer 2 · 2022-04-07T16:00:11+02:00

Penelope has to pay $11.8 for a mug with her own name on it.

Number of letters in Alexander's name = 9

Number of letters in Lucia's name =5

The Difference in the number of letters in both the names

= 9-5

=4 letters

Alexander pays = $12.60

Lucia pays = $9.40

Difference in payments = 12.60-9.40 = $3.20

It means charge for 4 letters = $3.20

So, charge for 1 letter = $0.80

Number of letters in Penelope's name = 8

So, Penelope will pay = 8*0.80 +fixed fee for the mug

= $6.4 +fixed fee for the mug

What will be the fixed fee for the mug?

The Fixed fee for the mug will be the payment done by Penelope for either Alexander or Lucia minus the charge for each word in the word Alexander or Lucia respectively.

The Fixed fee for the mug = $9.40 - charge for each word in the word "Lucia"

The Fixed fee for the mug = 9.40 - 5*0.80 = $5.40

So, Penelope will pay = 6.4 +5.4 =$11.8

Therefore, Penelope has to pay $11.8 for a mug with her own name on it.

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