Introduction to writing and solving linear equations in one variable - item 2737
questionz
you buy 8 packs of markers with 20 markers in each pack, you already had 10
markers, which equation shows how to calculate the total number of markers, m, you
have?
clear
check
m = 20. 8 - 10
m = 10.8 + 25
m = 8.20 + 10
m = 8 + 10

m = 8.20 + 10 is the equation that shows the total number of markers.

Step-by-step explanation:

Number of packets of markers purchased  = 8

Number of markers in each packet = 20

⇒Total numbers of markers purchased =  Total packets x Markers in each              

                                                                                                           pack

= 20 x 8

Number of markers already there = 10

⇒ The TOTAL NUMBER OF MARKERS (m)

= Number of markers purchased + Number of markers already at home

or, total markers  m =  (20 x 8)  +  10

Hence, m = 8.20 + 10 is the equation that shows he total number of markers.

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

equation image indicator

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

equation image indicator

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!

step-by-step explanation: