Easy trading, complicated process

Algebra Level pending

If one math book is sold from Alex's store, three roses are sold from Bill's store. For each pen he sells, he sells a rose. If five pens are sold from Bill's store, twenty chocolates are also sold from Alex's store.

One day, if Alex sells a total of sixty chocolates, then how many math books were sold from his store?


The answer is 5.

Soha Farhin Pine Pine by Soha Farhin Pine Pine , 18, Bangladesh

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1 solution

Let M B MB represent math books, R R roses, P P pens, and C C chocolates.

According to the problem statement,

  • When Alex sells 1 M B 1MB , Bill sells 3 R 3R .

  • When Bill sells 1 P 1P , Bill also sells 1 R 1R .

  • When Bill sells 5 P 5P , Alex sells 20 C 20C .

If, one day, Alex sells 60 chocolates (which is 3 times 20 chocolates), Bill sells 15 pens.

Alex: ( 20 × 3 ) C (20 \times 3)C → Bill: ( 5 × 3 ) P (5 \times 3)P

Alex: 60 C 60C → Bill: 15 P 15P

Then Bill sells 15 roses as well, since 

For each pen he sells, he sells a rose.

Bill: ( 5 × 3 ) R (5 \times 3)R → Alex: ( 5 × 3 3 ) M B (\frac{5 \times 3}{3})MB

Bill: 15 R 15R → Alex: 5 M B 5MB

Therefore, Alex sells 5 \boxed{5} math books on that very day.

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