Easy #6

Geometry Level 1

Australia has rectangular currency notes for $ 5 , $ 10 , $ 20 , $ 50 \$5, \$10, \$20, \$50 and $ 100 \$100 . These notes are all 65 65 mm wide but each note is 7 7 mm longer than the note of the next lowest value. What is the difference in area, in square millimetres, between the $10 note and the $100 note?


The answer is 1365.

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Victor Loh by Victor Loh , 19, Singapore

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4 solutions

Tom Dufall
Jul 27, 2014

The $100 note is 3 divisions higher than the $10 note, so is 7*3=21mm longer.

The extra area is therefore the extra length*width,

21*65=1365

8 Helpful 0 Interesting 0 Brilliant 0 Confused

what is the length ?

Nasser Hameed - 6 years, 10 months ago

I agreed with Tom Dufall answer.

Nasser Hameed - 6 years, 10 months ago

Simple method. Gud try!

Christo George - 6 years, 10 months ago
Ruel Ranay
Oct 6, 2014

if $5 is 7mm long, then the next note would be 14mm... then, 65 * 14 = 910 sq mm...

next, the length of the $100 note would be 35mm... then, 65 * 35 = 2275 sq mm...

by subtracting the areas of the $10 and $100 notes... 2275 - 910 = 1365 (ans)

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Parth Dwivedi
Sep 6, 2014

The 100 note is longer than 10 note as it is 3 divisions higher (7×3=21).

Let x be the length of 10 note.

ATQ

65×(x+21)-65x

=65 (x+21-x)

=65×21

=1365

Thus the answer is 1365.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Rifath Rahman
Aug 1, 2014

Let the length of $10 be x,so the length of the $ 100 becomes=3 * 7+x(As $ 100 is 3 division higher than $ 10)=21+x.Now the area of the $ 100=(21+x) * 65=1365+65x,and the area of the $ 10 is (x * 65)=65x. So $ 100 is (1365=65x-65x)=1365 more than $ 10

0 Helpful 0 Interesting 0 Brilliant 0 Confused

65(x+7)-65(x+7+7+7+7) 65x+455-(65x+1820) 455-1820 -1365

gautam sachdeva - 6 years, 10 months ago

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