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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?

Respuesta :

4 packs of bottled water (35*4=140)
7 packs of candy bars (20*7=140)

Answer:

4 packs of water and 7 packs of candy bars.

Step-by-step explanation:

We want to know the smallest number that both 35 and 20 will go into.  This is the least common multiple (LCM).

To find the LCM, we find the prime factorization of each number:

35 = 5(7)

20 = 5(4)

4 = 2(2)

20 = 5(2)(2)

We now multiply the common factor, 5, by all of the uncommon factors:

5(7)(2)(2) = 35(2)(2) = 70(2) = 140

This means she needs 140 bottles of water and 140 candy bars.

Water is sold in packs of 35; this means she needs

140/35 = 4 packs of water.

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

140/20 = 7 packs of candy bars.

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