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30 cans of paint A or 50 cans of paint B are required to paint a wall.

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30 cans of paint A or 50 cans of paint B are required to paint a wall.  [#permalink]

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New post 08 Sep 2018, 03:01
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Question Stats:

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30 cans of paint A or 50 cans of paint B are required to paint a wall. If x cans of paint A and 30 cans of paint B are used to paint the same wall,what is the value of X?

A. 9
B. 12
C. 15
D. 18
E. 24
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30 cans of paint A or 50 cans of paint B are required to paint a wall.  [#permalink]

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New post 08 Sep 2018, 07:27
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OA:B

\(30\) cans of Paint A can paint \(1\) wall

\(1\) can of Paint A can paint \(\frac{1}{30}\) wall

\(X\) cans of Paint A can paint \(\frac{X}{30}\) wall

\(50\) cans of Paint B can paint \(1\) wall

\(1\) can of Paint B can paint \(\frac{1}{50}\) wall

\(30\) cans of Paint B can paint \(\frac{30}{50}\) wall

According to question stem

\(\frac{X}{30}+ \frac{30}{50} = 1\)

\(\frac{X}{30} = 1 - \frac{30}{50}\)

\(\frac{X}{30} = \frac{20}{50}\)

\(X = \frac{20*30}{50}=12\) cans
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30 cans of paint A or 50 cans of paint B are required to paint a wall.  [#permalink]

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New post 08 Sep 2018, 10:52
Yashaz91 wrote:
30 cans of paint A or 50 cans of paint B are required to paint a wall. If x cans of paint A and 30 cans of paint B are used to paint the same wall,what is the value of X?

A. 9
B. 12
C. 15
D. 18
E. 24

Think in terms of one wall.
1) 30 cans of B cover what portion of 1 wall?

ONE wall requires 50 cans of paint B
Only 30 cans were used.
\(\frac{50}{50}\) cans used = 1 whole wall painted
\(\frac{30}{50}\) cans used = \(\frac{3}{5}\) of one wall is painted

2) What portion of the wall is not painted?
\((1W-\frac{3}{5}W)=\frac{2}{5}W\)

3) How many cans of A are needed?

One wall requires 30 cans of A.
\(\frac{2}{5}\) of 1 wall requires how many cans of A?
If 30 cans of A can paint one whole wall, then \(\frac{2}{5}\) of one wall will require \(\frac{2}{5}\) the amount of paint.*
\((\frac{2}{5}*30)=12\) cans of A

Answer B

*\(\frac{30}{1}=\frac{A}{(\frac{2}{5})}\)
\(A=(30*\frac{2}{5})=12\)

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30 cans of paint A or 50 cans of paint B are required to paint a wall.  [#permalink]

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New post 08 Sep 2018, 20:43
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1
Yashaz91 wrote:
30 cans of paint A or 50 cans of paint B are required to paint a wall. If x cans of paint A and 30 cans of paint B are used to paint the same wall,what is the value of X?

A. 9
B. 12
C. 15
D. 18
E. 24


\(30a = 50b\)

\((xa + 30b) = 50b\)
\(xa = 20b\)

x= 12
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30 cans of paint A or 50 cans of paint B are required to paint a wall.   [#permalink] 08 Sep 2018, 20:43
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