Mira is making telescopes, each consisting of 2 lenses, 1 tube, and 1 eyepiece. Lenses can be purchased only in packs of 50, tubes only in packs of 10, and eyepieces only in packs of 30. However, half of the lenses in each pack are not usable for telescopes. If all parts are used only for the telescopes, what is the minimum number of lenses Mira must purchase to make a set of telescopes with no leftover components other than the unusable lenses?

Question

Terrence Ross

Mathematics

10 October, 01:37

Mira is making telescopes, each consisting of 2 lenses, 1 tube, and 1 eyepiece. Lenses can be purchased only in packs of 50, tubes only in packs of 10, and eyepieces only in packs of 30. However, half of the lenses in each pack are not usable for telescopes. If all parts are used only for the telescopes, what is the minimum number of lenses Mira must purchase to make a set of telescopes with no leftover components other than the unusable lenses?

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Answers (1)

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Aryana Rocha · Answer 1

The minimum number of lenses that Mira must purchase is = 12 packs=600 lenses

Step-by-step explanation:

You know that one Telescope is made for:

2 lenses (they are purchased by packs of 50 (only 25 works for Telescopes)

1 tube (they are purchased by packs of 10)

1 eyepiece (they are purchased by packs of 30)

Then the minimum number of lenses Mira must purchase to make a set of telescopes with no leftover components other than the unusable lenses, should be a whole number that is divisible by 30 and 10.

You can calculate how many packs Mira Needs to purchased in order to find that number.

You Know that 2 lenses are needed for 1 Telescope and that they are purchased by packs of 50 where only 25 works for Telescopes

Then you can express that how:

Number of telescopes Mira can make from Lenses = (50/4) * Number of packages of lenses

Then If Mira purchases:

1 pack of lenses, she can make 12.5 telescopes (it's no divisible by 30 and 10)

2 packs of lenses, she can make 25 telescopes (it's no divisible by 30 and 10)

3 packs of lenses, she can make 37,5 telescopes (it's no divisible by 30 and 10)

4 packs of lenses, she can make 50 telescopes (it's no divisible by 30 and 10)

5 packs of lenses, she can make 62,5 telescopes (it's no divisible by 30 and 10)

6 packs of lenses, she can make 75 telescopes (it's no divisible by 30 and 10)

7 packs of lenses, she can make 87,5 telescopes (it's no divisible by 30 and 10)

8 packs of lenses, she can make 100 telescopes (it's no divisible by 30 and 10)

9 packs of lenses, she can make 112,5 telescopes (it's no divisible by 30 and 10)

10 packs of lenses, she can make 125 telescopes (it's no divisible by 30 and 10)

11 packs of lenses, she can make 137,5 telescopes (it's no divisible by 30 and 10)

12 packs of lenses, she can make 150 telescopes (it's a whole number and is divisible by 30 and 10)

Then she needs to purchase 600 lenses, 5 packs of eyepieces and 15 packs of tubes in order to make 150 Telescopes.