Miguel and his brother ario are both standing 3 meters from one side of a 25-meter pool when they decide to race. miguel offers ario a head start. miguel says he will start when the ratio of ario's completed meters to ario's remaining meters is 1: 4. how many meters will ario swim before miguel starts the race? round to the nearest tenth. meters

Miguel start to swim when Ario has traveled 4.4 m.

Step-by-step explanation:

The total lenght of the pool is 25.

Since both of them standing 3 m from one side of the pool, then, the total distance both need to cover is m= 22 m.

Assume that the distance traveled by Ario before Miguel start to swin is . That means, the remaining distance to Ario (to cover the total size of the pool) is .

Then, in acoordance to the problem, the ratio between these two distances must be equal to 1/4.

That is,

.

So, we need to obtain from this equation. We must note that , otherwise we have a zero in the denominator.

So, we rearrange the equation,

(Multiplying both sides of equation by ().

Then, .

Therefore, m.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

50-38=12

step-by-step explanation: