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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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Joined: 08 Sep 2018
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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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08 Sep 2018, 03:01
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45% (medium)

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61% (01:48) correct 39% (01:51) wrong based on 51 sessions

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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
Senior Manager
Joined: 22 Feb 2018
Posts: 422
30 cans of paint A or 50 cans of paint B are required to paint a wall.  [#permalink]

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08 Sep 2018, 07:27
1
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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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

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

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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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08 Sep 2018, 20:43
1
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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30 cans of paint A or 50 cans of paint B are required to paint a wall.

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