+0  
 
0
1124
4
avatar+1793 

A school orders 99 textbooks, all for the same price. When the bill for the total order comes, the first and last digits are obscured, and the cost of the textbooks reads $\$-{,}112.7-$. What is the total combined cost of the textbooks?

Mellie  Jul 24, 2015

Best Answer 

 #1
avatar+93665 
+20

Hi Mellie

All pronumerals that I use in this question have integer values.

A1127B = 99C

100000A+11270+B=99C

99×1010A+10A +99×113+83+B=99C

99(1010A+113)+10A+83+B=99C

10A+B+83=99(C-1010A-113)

10A+B+83=99D

10A+B=99D-83

Now A and B are both single digit numbers so D can only equal 1.

 

10A+B=16

A=1 and B=6

The price is    111276 cents or

$1112.76

The books were $11.24 each.

Melody  Jul 25, 2015
 #1
avatar+93665 
+20
Best Answer

Hi Mellie

All pronumerals that I use in this question have integer values.

A1127B = 99C

100000A+11270+B=99C

99×1010A+10A +99×113+83+B=99C

99(1010A+113)+10A+83+B=99C

10A+B+83=99(C-1010A-113)

10A+B+83=99D

10A+B=99D-83

Now A and B are both single digit numbers so D can only equal 1.

 

10A+B=16

A=1 and B=6

The price is    111276 cents or

$1112.76

The books were $11.24 each.

Melody  Jul 25, 2015
 #2
avatar+90023 
+5

That's a very crafty way to solve that problem, Melody.....I wouldn't have thought of that......!!!!

 

 

CPhill  Jul 30, 2015
 #3
avatar+93665 
0

Thanks Chris,     

It was a great little problem :)

Melody  Jul 30, 2015
 #4
avatar+27044 
+10

Good reasoning Melody.

Here's an alternative approach as a check:

 Cost of books:

.

Alan  Jul 30, 2015

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