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Most people answer $$ a = b + \frac{40}{100}b $$

but I think this should also be right $$ a - \frac{40}{100}a = b $$ Is one of them wrong or both are correct?
Or the statement is lacking details of 40% of who (b or a).

Help me solve this question. Thanks.

miracle173
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Astrid Morales
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    Technically I would say it is lacking detail, grammatically I would say the first one. – Paul Feb 08 '22 at 15:31
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    "equation is greater" makes no sense. The value of a is greater than b by 40% makes sense – miracle173 Feb 08 '22 at 15:34
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    "by 40%" is not specific enough. If it were clarified we would specify "by 40% of b" or "by 40% of a" or even "by 40% of c" for some other value $c$ and this would remove all ambiguity. That said, the phrase without clarification does sadly appear in everyday language at times. Usually in such a case, "of b" is intended. – JMoravitz Feb 08 '22 at 15:37
  • @miracle173 I think the OP means something like: The equation for "a is 40% greater than b". – Jaap Scherphuis Feb 08 '22 at 15:44
  • @JaapScherphuis Yes, that is possible. I will edit the title – miracle173 Feb 08 '22 at 15:47

2 Answers2

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This phrase always means that $a$ is $100$% of $b$ plus $40$% of $b$. Thus, your first thought is correct.

Some Guy
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The phrasing is not clear. Let me rephrase:

$$\textrm{"a is greater than b by 40%"}$$

Let start with the untrue equality $a=b\quad(1) $.

At the moment the LHS is greater than the RHS by $40\%$. To obtain an equality we add $40\%$ on the right side.

$$a=b+0.4\cdot b\Rightarrow \boxed{a=1.4b}$$

Next we can set up an equation for $\textrm{"b is smaller than a by 40%"}$. If we look at $(1)$ we have to subtract $40\%$ at the left side to obtain a true equality.

$$a-0.4a=b\Rightarrow \boxed{0.6a=b}$$ It is worth to notice that this two equations are not equivalent (equal).

callculus42
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