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

#1**+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**+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