Question

The manager of a snack bar buys bottled water in packs of 35 and candy bars in packs of 20. Then, she sells the items individually. Yesterday, she bought the same number of water bottles as candy bars to sell at the snack bar. If she bought the lowest number of items possible, how many packs of each item did she buy?

Answer 1

$\Huge\bf{\underline{\red \dag { Aиѕωєя }}} \red \dag$

4 Packs of water and 7 Packs of candy bars.

So, we wanna know the smallest number that both 35 and 20 will go into.

Find the Least Common Multiple (LCM), but to find the LCM we need to find the prime factorization of each of the following number :-

$\sf {35 = 5(7)}$

$\sf \red {20 = 5(4)}$

$\sf {4 = 2(2)}$

$\sf \red {20 = 5(2)(2)$

~Now multiply all the numbers by 5 :-

$\sf \pink{5(7)(2)(2) = 35(2)(2) = 70(2) = 140}$

This means she needs 140 bottles of water and 140 candybars.

Water is sold in packs of 35, this means that she needs :

$\sf \orange{ \frac{140}{35} = 4\: packs \: of \: water}$

Candy bars are sold in packs of 20, this means she needs :

$\sf \green{ \frac{140}{20} = 7 \: packs \: of \: candy \: bars}$

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