6) when a teacher counted her students in groups of 4, there were 2 students left over. when she counted them in groups of 5, she had 1 student left over. if 15 of her students were girls, and she had more girls than boys, how many students did she have? ?

this needs to be shown full work for full credit on my college math class i need it’s due this !

The solution is that there are 26 students in her class

Step-by-step explanation:

We know that 15 of her student are girls, and since there are more girls than boys in the class, there can at most be 15+14= 29 students in her class.

We need to find a number x between 16 (in the case where there is only one boy in the class) and 29, for which x/4 gives a remainder of 2, and x/5 gives a remainder of 1.

The numbers between 16 and 29, which when divided by 4 gives a remainder of 2 are:

18, 22, and 26

You can check yourself that these give a remainder of 2.

So it is one of these numbers. But the solution must also fulfill that the number divided by 5 gives a remainder of 1.

18/5 = 15 + remainder=3

22/5 = 4 + remainder=2

26/5 = 5 + remainder=1

Thus the only possible solution is 26.

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!