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3 years ago

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Pixel goes shopping with one hundred dollars and ends up buying three different types of items: A, B, and C. The unit price of A

is five dollars, B is 25 cents, and C is five cents. Pixel comes home and finds that all the money had been spent, but discovers that the total number of items is exactly equal to100. How many items of each kind did Pixel buy? No fractions allowed. (Spend exactly 100 dollars and buy a total of 100 items)

1 answer:

mixas84 [53]3 years ago

5 0

Answer:

A - 16, B - 79, C - 5

Step-by-step explanation:

<u>Given</u>

A costs 5$
B costs $0.25
C costs $0.05
A + B + C = 100
5A + 0.25B + 0.05C = 100 ⇒ 100A + 5B + C = 2000

<u>Subtract the first equation from the second:</u>

99A + 4B = 1900

<u>We have a restriction in numbers:</u>

0 < A, B, C < 100

<u>Since 4B can be max 400, we get 99A > 1500 and 99A < 1900 so:</u>

A > 1500/99 > 15

and

A < 1900/99 < 19

A can be 16 or 18 as it should be even number to get B the whole number.

<u>If A = 16:</u>

99*16 + 4B = 1900
4B = 1900 - 1584
4B = 316
B = 316/4 = 79

<u>If A = 18:</u>

99*18 + 4B = 1900
4B = 1900 - 1782
4B = 118
B = 118/4 = 29.5, discarded as decimal

<u>So we get:</u>

A = 16, B = 79 and C = 100 - (16 + 79) = 5

<u>Let's proof the numbers:</u>

16*5 + 79*0.25 + 5*0.05 = 100, confirmed

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